AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

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AP State Syllabus 10th Class Maths Bits 10th Lesson Mensuration with Answers

Question 1.
The total surface area of a cube is 54 cm2, then find its side.
Answer:
3 cm
Explanation:
TSA = 6s2 = 54
⇒ side2 = 9 ⇒ side = 3 cm.

Question 2.
Base area of a regular cylinder is 154 cm2, then find its radius.
Answer:
7 cm
Explanation:
πr2 = 154
⇒ r2 = 154 × \(\frac{7}{22}=\frac{14 \times 7}{2}\) × 7 × 7
⇒ r = 7 cm

Question 3.
If the height and radius of a cone are 15 cm and 8 cm, then find its slant height
Answer:
17 cm
Explanation:
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 1

Question 4.
Write a formula to find curved surface area of a hemisphere.
Answer:
2πr2

Question 5.
How much the volume of a cube having 1 cm side ?
Answer:
1 cm3

Question 6.
Ratio of volumes of two spheres is 8 : 27, then find ratio of their curved surface area.
Answer:
4 : 9
Explanation:
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 2
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 3

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 7.
Football is in a model of …………..
Answer:
sphere

Question 8.
If the volume of a cube is 216 cm3, then find its side.
Answer:
6 cm
Explanation:
S3 = 216 ⇒ Side = \(\sqrt[3]{216}\) = 6 cm

Question 9.
Find the curved surface area of a right circular cylinder.
Answer:
2πrh

Question 10.
Find the curved surface area of a sphere will be……………. whose radius
is 10 cm.
Answer:
400 π

Question 11.
Find the volume of a cube will be ………….. (in cm3), whose total surface area is 216 cm2.
Answer:
216
Explanation:
6S2 = 216
⇒ S2 = \(\frac{216}{6}\) = 36
⇒ S = \(\sqrt{36}\) = 6
∴ Volume = S3 = 63 = 216

Question 12.
Write the name of a famous book writ-ten by ancient mathematician Aryabhatta.
Answer:
Aryabhatteeyam.

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 13.
Which of the following vessel can be filled with more water (A, B are in cylindrical shape)?
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 4
Answer:
B)

Question 14.
Find the volume of right circular cylinder with radius 6 cm and height 7 cm.
Answer:
792 cm3

Question 15.
A sphere of radius ‘r’ inscribed in a cylinder. The surface area of the sphere …………… of the cylinder.
Answer:
Curved surface area.

Question 16.
How much the maximum length of the stick that can be placed in a cuboid, whose measurements are 8 × 4 × 1?
Answer:
9

Question 17.
A cylinder and cone have bases of equal radii and are of equal heights, then find their volumes are in the ratio.
Answer:
3 : 1

Question 18.
Find the total surface area of a solid hemisphere of radius 7 m.
Answer:
147 π sq.m.
Explanation:
3πr2 = 72 × 3 × π = 147π sq.m.

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 19.
Radius of a cone is ‘r’, height is ‘h’ and its slant height is ‘l’, then which of the following is false ?
Answer:
Always r > p

Question 20.
Radius, height, slant height of a cone are r, h, ‘l’, then 7′ value in terms of r and h.
Answer:
\(\sqrt{r^{2}+h^{2}}\)

Question 21.
Volumes of two spheres are in the ratio of 8:27. Find the ratio of their surface areas.
Answer:
4 : 9

Question 22.
A solid ball is exactly fitted inside the cubical box of side ‘a’. Find the volume of the ball.
Answer:
\(\frac{1}{6}\) πa3

Question 23.
If the total surface area of cube is 96 cm3, then find side of cube.
Answer:
4 cm

Question 24.
Base area of the prism is 30 cm2 and its height is 10 cm. Then find the volume of the prism.
Answer:
300 cm3

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 25.
The volume of a cone with base radius 7 cm is 462 c.c., find its height.
Answer:
9 cm

Question 26.
If total surface area of a cube is 96 cm2, then find its volume.
Answer:
64 cm3

Question 27.
Find the volume of cone, whose radius is 3 cm and height is 8 cm.
Answer:
24 π

Question 28.
Write a formula to find total surface
area of cone in sq. units. f
Answer:
πr2 + πrl

Question 29.
Find the volume of a hemisphere of radius 3.5 cm is …………… cm3.
Answer:
89.83

Question 30.
In the above problem find TSA = ………………… cm2.
Answer:
115.5

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 31.
Write a combination of a shuttle cock.
Answer:
Hemisphere, frustum cone

Question 32.
The volume of cone is 462 cm3, r = 7 cm, then find h is ……………… cm.
Answer:
9

Question 33.
103 (cm)3 = ……………. litre.
Answer:
1

Question 34.
In l2 = h2 + r2, h = 15, r = 8, then l = ………………
Answer:
17

Question 35.
The perimeter of an equilateral triangle is 60 cm, then find its area (in cm2).
Answer:
173.2

Question 36.
Write the number of faces of a cuboid.
Answer:
8

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 37.
If the ratio of radii of two spheres is 2:3, then find the ratio of their surface areas.
Answer:
4 : 9

Question 38.
Write a formula to find volume of sphere in …………….. cu. units.
Answer:
\(\frac{4}{3}\)πr3

Question 39.
In a hollow cuboid box of size 4 × 3 × 2 m, find the number of solid iron spherical balls of radius 0.5 m that can be packed.
Answer:
24

Question 40.
In a cone, r = 7 cm, h = 10 cm, then find l = cm.
Answer:
12.2

Question 41.
Find T.S.A of a solid hemisphere whose radius is 7 cm.
Answer:
147π

Question 42.
Find the total surface area of hemisphere of radius ’r’.
Answer:
3πr2

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 43.
If the length of each diagonal of a cube is doubled, then how many times its volume becomes.
Answer:
8

Question 44.
Who gave the symbol π?
Answer:
Euler

Question 45.
Find the surface area of a cube, whose side is 27 cm.
Answer:
4374 cm3

Question 46.
Find the volume of cone if r = 2 cm, h= 4 cm.
Answer:
\(\frac{16}{3}\)π cm3
Explanation:
Volume of cone = \(\frac{1}{3}\) πr2h
\(\frac{1}{3}\) × π × 4 × 4 = \(\frac{16}{3}\)π cm3

Question 47.
Write the number of edges of a cuboid has.
Answer:
12

Question 48.
Find the volume of a right circular cone with radius 6 cm and height 7 cm is …………….. cm3.
Answer:
264
Explanation:
Volume of right circular cone V = \(\frac{1}{3}\) πr2h
= \(\frac{1}{3}\) . π . 62 . 7 = 264 cm3.

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 49.
If a right angled triangle is revolved about its hypotenuse, then find it will form a ……………..
Answer:
Double cone

Question 50.
Write a formula to find CSA of cylinder ……………… sq. units.
Answer:
2πrh

Question 51.
Volume of cuboid = ………….. cu.units.
Answer:
lbh

Question 52.
Write a formula to find surface area of sphere ……………. in sq. units.
Answer:
4πr2

Question 53.
Total surface area of a cube is 216 cm2, then find its volume.
Answer:
216

Question 54.
If the radii of circular ends of a frustum of a cone are 20 cm and 12 cm and its height is 6 cm, then find the slant height of the frustum.
Answer:
10

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 55.
If the external and internal radii of a hollow hemispherical bowl are R and r, then find its total surface area.
Answer:
π (3R2 + r2)

Question 56.
Rational value of π = …………………
Answer:
22/7

Question 57.
A cylinder, a cone and a hemisphere are of equal base and have the same height, then find the ratio of their volumes.
Answer:
3 : 1 : 2
Explanation:
Cylinder, Cone, Hemisphere have equal base and same height. So, the height will become radius.
= Volume of cylinder: Volume of cone : Volume of hemisphere
= πr2h : \(\frac{1}{3}\) πr2h : \(\frac{2}{3}\) πr2h
= \(\frac{1}{3}\) πr3 : \(\frac{2}{3}\) πr3 : πr3
= 1 : \(\frac{1}{3}\) : \(\frac{2}{3}\) = 3 : 1 : 2

Question 58.
A solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then find radius of small spherical balls.
Answer:
5
Explanation:
Volume of sphere = 8 (volume of one spherical ball)
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 5

Question 59.
Write a formula to find CSA of cone = ………………… sq. units.
Answer:
πrl

Question 60.
Find the total surface area of a solid hemisphere of radius 7 cm.
Answer:
239π cm2

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 61.
The volume of a vessel in the form of a right circular cylinder is 448π cm3 and its height is 7 cm, then find the radius of the base.
Answer:
8 cm

Question 62.
If the diameter of a sphere is’d’, then find its volume.
Answer:
\(\frac{1}{6}\) πd2

Question 63.
Write a formula to find total surface area of cylinder in ……………….. sq. units.
Answer:
2πrh+ 2πr2

Question 64.
In a cylinder, r= 7 m, h=15 m, then find V.
Answer:
2310 m3.

Question 65.
If the diagonals of a rhombus are 10 cm and 24 cm, then find area in ………………… cm2.
Answer:
120

Question 66.
Find the curved surface area of a right circular cone of height 15 cm and base diameter is 16 cm.
Answer:
136π cm2

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 67.
Find the number of balls, each of radius 1 cm that can be made from a solid sphere of radius 8 cm.
Answer:
512

Question 68.
Volume of hemisphere is19404 cm3, then find its TSA (in cm2).
Answer:
4158

Question 69.
r3 = 1728, then find ‘r’.
Answer:
12

Question 70.
In a cone, d = 14 cm, l = 10 cm, then find CSA = ……………….. cm2.
Answer:
220

Question 71.
In the figure, P = …………………
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 6
Answer:
h2 + r2

Question 72.
The surface area of a sphere is 616 sq.cm, then find its radius in …………. cm.
Answer:
7

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 73.
In a hemisphere, r = 7 cm, then find CSA (in cm2)
Answer:
308

Question 74.
Write a formula to find volume of hollow cylinder.
Answer:
(πR2 – r2)

Question 75.
In a cube, a = 4 cm, then find TSA (in cm2).
Answer:
90

Question 76.
In a cylinder, h=14 cm, V= 176 cm3, r = …………….. cm.
Answer:
2

Question 77.
In a hemisphere, r = 1.75 cm, then find CSA (in cm2).
Answer:
38.5

Question 78.
TSA of a cylinder is 1188 cm2, h = 20 cm (in cm), then find its volume.
Answer:
3080

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 79.
Heap of stones is an example of ………………
Answer:
Cone

Question 80.
Write a formula to find diagonal of rectangle.
Answer:
\(\sqrt{l^{2}+b^{2}}\)

Question 81.
The area of the base of a right circular cone is 78.5 cm2. If its height is 12 cm, then find its volume (in cm3).
Answer:
314

Question 82.
Surface area of a sphere and cube are equal, then find the ratio of their volumes.
Answer:
√π : √6
Explanation:
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 7

Question 83.
A conical flask is full of water. The flask has base radius r and height h. The water is poured into a cylindrical flask of base radius mr. Find the height of water in the cylindrical flask.
Answer:
\(\frac{\mathrm{h}}{3}\) m2

Question 84.
Find the volume of the greatest cylinder that can be cut from a solid wooden cube of length of edge 14 cm.
Answer:
2156 cm3

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 85.
The area of equilateral triangle is 36√3 cm2, then find the perimeter (in etn).
Answer:
36
Explanation:
Area 36√3 cm2 ⇒ \(\frac{\sqrt{3} a^{2}}{4}\) = 36√3
⇒ a2 = 36 × 4
⇒ a = 6 × 2 = 12 cm
Perimeter = 3a = 3 × 12 = 36 cm.

Question 86.
Base circumference of a cylinder is 220 cm and height is 63 cm, then find CSA (in cm2).
Answer:
13860

Question 87.
Write a formula to find area of equi¬lateral triangle of side ‘a’ units (in sq. units).
Answer:
\(\frac{\sqrt{3}}{4}\)a2

Question 88.
A solid iron cuboid of dimensions 49 × 33 × 24 cm is melted to form a solid sphere, then find its radius.
Answer:
21 cm

Question 89.
A cone and a hemisphere have equal bases and equal volumes, then find the ratio of their heights.
Answer:
2 : 1

Question 90.
Laddu is an example of ……………
Answer:
Sphere

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 91.
Write a formula to find total surface area of a cube (in sq. units).
Answer:
6l2

Question 92.
The height of a cylinder is doubled and radius is tripled, then how many times its curved surface area will become.
Answer:
6 times
Explanation:
CSA of cylinder is 2πrh, if radius is tripled and height is doubled, then CSA = 2π . 3r . 2h = 12πrh = 6(2πrh)

Question 93.
Write a formula to find volume of hemisphere (in cu. units).
Answer:
\(\frac{2}{3}\)πr3

Question 94.
The surface areas of two spheres are in the ratio 1 : 4, then find ratio of their volumes.
Answer:
1 : 64

Question 95.
Write the diameter of a sphere which can inscribe a cube of edge ‘x’ cm.
Answer:
x

Question 96.
The volume of a cube is 216 cm3, then find its edge.
Answer:
6

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 97.
Write a formula find volume of cylinder (in cu. units).
Answer:
πr2h

Question 98.
Find the ratio of volume of a cone and cylinder of equal diameter and height.
Answer:
1 : 3

Question 99.
Write a formula to find volume of a cube (in cu. units).
Answer:
a3

Question 100.
The sphere of radius 2.1 cm, then find its volume (in cm3).
Answer:
38.08

Question 101.
A sphere, a cylinder and a cone have the same radius, then find the ratio of their curved surface areas.
Answer:
4 : 4 : √5

Question 102.
If the diagonal of a cube is 2.5 m, then find its volume (in m3).
Answer:
\(\frac{5.2}{\sqrt{3}}\)
Explanation:
Applying Pythagoras theorem,
(2.5)2 = [a2 + (√2a)2]
⇒ 6.25 = 3a2
⇒ a2 = \(\frac{6.25}{3}\) ⇒ a = \(\frac{2.5}{\sqrt{3}}\) m3
Volume of cube = a3
\(\left(\frac{2.5}{\sqrt{3}}\right)^{3}\) = \(=\frac{15.625}{3 \sqrt{3}}=\frac{5.2}{\sqrt{3}}\) m3

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 103.
A heap of rice is in the form of a cone of diameter 12 m and height 8 m, then find the volume (in m3).
Answer:
301.71

Question 104.
Perimeter of square is 20 cm, find then area (in cm2).
Answer:
25

Question 105.
CSA of a cone is 4070 cm2 and its diameter is 70 cm, then find slant height.
Answer:
37

Question 106.
The volume of a cuboid is 3,36,000 cm3. If its area is 5,600 cm2, then find h. (in cm).
Answer:
60

Question 107.
Write a formula to find diagonal of a cuboid.
Answer:
\(\sqrt{l^{2}+b^{2}+h^{2}}\)

Question 108.
Find the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm.
Answer:
19.4 cm3

Question 109.
The diameter of a metallic sphere is 6 cm and melted to draw a wire of diameter 2 cm, then find the length of the wire.
Answer:
9 cm
Explanation:
Volume of sphere = Volume of cylinder
\(\frac{4}{3}\)πr3 = πr2h
⇒ \(\frac{4}{3}\) × 33 = h × 22
⇒ 4 × 9 = h × 4 ⇒ h = 9 cm

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 110.
The volume and surface area of a sphere are numerically equal. Then find the volume of the smallest cylinder in which the sphere is exactly kept.
Answer:
54π

Question 111.
Write a formula to find volume of cone with’d’ as diameter and ’h’ as height is ………………. cu. units.
Answer:
\(\frac{\pi \mathrm{d}^{2} \mathrm{~h}}{12}\)

Question 112.
An iron cylindrical rod has a height 4 times its radius is melted and cast into spherical balls of the same radius. Find the number of balls cast.
Answer:
6
Explanation:
Volume of cylinder = n × Volume of sphere
πr2h = n × \(\frac{4}{3}\)πr3
πr2(8r) = n × \(\frac{4}{3}\)πr3
n = \(\frac{24}{4}\) = 6
∴ Number of balls = 6.

Question 113.
If a cone is cut into two parts by a horizontal plane passing through the mid point of the axis, find the ratio of the volumes of the upper part and the cone.
Answer:
1 : 8

Question 114.
In a cylinder, r = 8 cm, h = 10 cm, then CSA = ……………….. cm3
Answer:
\(\frac{3520}{7}\)

Question 115.
In a cone, (l + r)(l – r) = …………..
Answer:
h2

Question 116.
A solid sphere of radius r melted and recast into the shape of a solid cone of height r, then find radius of the base of the cone.
Answer:
2r

Question 117.
If the radius of base of a cylinder is doubled and the height remains un-changed, its C.S.A becomes.
Answer:
3 times

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 118.
Write a formula to find volume of cone, (in cu. units).
Answer:
\(\frac{1}{3}\)πr2h

Question 119.
Write a formula to find diagonal of a cube (in units).
Answer:
a√3

Question 120.
The ratio of volume of two cones is 4 : 5 and the ratio of the radii of their base is 2 : 3, then find ratio of their vertical heights.
Answer:
9 : 5

Question 121.
Find the number of cubes of side 2 cm which can be cut from a cube of side 6 cm.
Answer:
27

Question 122.
A cuboid has dimensions 10 × 8 × 6 cm, then find its volume (in cm3).
Answer:
480

❖ Choose the correct answer satisfying the following statements.
Question 123.
Statement (A): The slant height of the frustum of a cone is 5 cm and the difference between the radii of its two circular ends is 4 cm. Than the height of the frustum is 3 cm.
Statement (B) : Slant height of the frustum of the cone is given by
l = \(\sqrt{(\mathrm{R}-\mathrm{r})^{2}+\mathrm{h}^{2}}\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
i) Both A and B are true.
Explanation:
We have, L = 5 cm, R – r = 4 cm
∴ 5 = \(\sqrt{(4)^{2}+\mathrm{h}^{2}}\)
⇒ 16 + h2 = 25
⇒ h2 = 25 – 16 = 9
⇒ h = 3 cm
Hence, (i) is the correct option.

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 124.
Statement (A) : If the volumes of two spheres are in the ratio 27 : 8. Then their surface areas’are in the ratio 3 : 2.
Statement (B) : Volume of the sphere
= \(\frac{4}{3}\) πr3 and its surface area = 4πr3.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
iv) Both A and B are false.
Explanation:
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 8
Hence, (iv) is the correct option.

Question 125.
Statement (A) : Two identical solid cube of side 5 cm are joined end to end. Then total surface area of the resulting cuboid is 300 cm2.
Statement (B): Total surface area of a cuboid is 2(lb + bh + lh).
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
iii) A is false, B is true.
Explanation:
When cubes are joined end to end, it will form a cuboid.
∴ l = 2 × 5 = 10 cm, b = 5 cm and h = 5 cm
∴ Total surface area = 2 (lb + bh + lh) = 2(10 × 5 + 5 × 5 + 10 × 5)
= 2 × 125 = 250 cm2
Hence, (iii) is the correct option.

Question 126.
Statement (A) : The number of 90ms 1.75 cm in diameter and 2 mm thick if formed from a melted cuboid 10 cm × 5.5 cm × 3.5 cm is 400.
Statement (B) : Volume of a cylinder = πr2h cubic units and area of cuboid = (l × b × h) cu. units.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
i) Both A and B are true.
Explanation:
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 9
Hence, (i) is the correct option.

Question 127.
Statement (A) : The radii of two cones are in the ratio 2 : 3 and their volumes in the ratio 1 : 3. Then the ratio of their height is 3 : 2.
Statement (B) :
Volume of the cone = \(\frac{1}{3}\)πr2h
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
iii) A is false, B is true.
Explanation:
We have, ratio of volume
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 10
Hence, (iii) is the correct option.

Question 128.
Statement (A) : The curved surface area of a cone of base radius 3 cm and height 4 cm is 15 π cm2.
Statement (B): Volume of a cone = \(\frac{1}{3}\)πr2h
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
i) Both A and B are true.

Question 129.
Statement (A): If the surface area of a sphere is 616 cm2. Then its radius 6 cm.
Statement (B): Surface area of sphere = 4πr2sq. units.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
iii) A is false, B is true.

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 130.
Statement (A) : A hemisphere of radius 7 cm is to be painted outside on the surface of it. The total cost of painting at ₹ 5 per cm2 is ₹ 2300.
Statement (B): The total surface area of a hemisphere is 3πr2sq. units.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
iii) A is false, B is true.

Question 131.
Statement (A) : Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm2.
Statement (B): If r be the radius and ‘h’ be the height of the cylinder, then total surface area= (2πrh + 2πr2)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true, iv) Both A and B are false.
Answer:
i) Both A and B are true.
Explanation:
A and B both are correct and B is the correct explanation of the A.
Total surface area = 2πrh × 2πr2
= 2πrh × 2πr2
= 2πr(h + r)
= 2 × \(\frac{22}{7}\) × 14 (30 + 14)
= 88 (44) = 3872 cm2
Hence, (i) is the correct’option,

Question 132.
Statement (A): If the height of a cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.
Statement (B) : If r be the radius and h the slant height of the cone, then slant
height = \(\sqrt{\mathrm{h}^{2}+\mathrm{r}^{2}}\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
iii) A is false, B is true.
Explanation:
A is incorrect here, but B is correct.
Slant height = \(\sqrt{\left(\frac{14}{2}\right)^{2}+(24)^{2}}\)
= \(\sqrt{49+576}\)
= \(\sqrt{625}\) = 25
Hence, (iii) is the correct option.

Question 133.
Statement (A): If the radius of a cone is halved and volume is not changed, then height remains same.
Statement (B): If the radius of a cone is halved and volume is not changed then height must become four times of the original height.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
iii) A is false, B is true.
Explanation:
A is incorrect and B is correct.
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 11
as V1 = V2
∴ 4h1 = h2
Hence, (iii) is the correct option.

Question 134.
Statement (A): If a ball in the shape of a sphere has a surface area of 221.76 cm2, then its diameter is 8.4 cm.
Statement (B) : If the radius of the sphere be r, then surface area S = 4πr2,
i.e., r = \(\frac{1}{2} \sqrt{\frac{\mathrm{s}}{\pi}}\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
i) Both A and B are true.

Question 135.
Statement (A) : Number of spherical balls that can be made out of a solid cube of lead whose edge is 44 cm, each ball being 4 cm in diameter is 2541.
Statement (B) : Number of balls = \(\frac{\text { Volume of one ball }}{\text { Volume of lead }}\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
ii) A is true, B is false.

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 136.
Statement (A) : If the base area and height of a prism be 25 cm2 and 6 cm respectively, then its volume is 150 cm3.
Statement (B): Volume of a pyramid = \(\frac{\text { Basearea } \times \text { height }}{3}\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
i) Both A and B are true.
Explanation:
A and B both are correct, but B is not the correct explanation of the A.
Volume of a prism = Base area × height
= 25 × 6 = 150 cm3
Hence, (i) is the correct option.

❖ Read the below passages and answer to the following questions.
A tent is in the form of a right circular cylinder, surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11m, while the vertex of the cone is 16 m above the ground.

Question 137.
The curved surface area of the cylindrical portion is
Answer:
(264π) m2
Explanation:
R = Radius = \(\frac{24}{2}\) = 12 m.
H = Height = 11 m.
Curved surface area of the cylindrical portion = 2πRH
= 2π(12)(11) = (264 π)m2.

Question 138.
The slant height of the cone is
Answer:
13 m
Explanation:
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 12
h = Height of the cylindrical portion
= 16 – 11 = 5m .
Slant height,
L = \(\sqrt{h^{2}+R^{2}}\) =\(\sqrt{25+144}\) = 13 m

Question 139.
The area of the canvas required for the tent is
Answer:
1320 m2
Latha said “Cuboid is one of right prism”.
Explanation:
Area of canvas required for the tent = Curved surface area of the cylindrical portion + Curved surface area of the cone
Surface area = 2πrh + πrl
= πr(2h + l)
= \(\frac{22}{7}\) × 12 (22 + 13)
\(\frac{264}{7}\) (22 + 13)
\(\frac{264}{7}\) × 35
= 132 cm 2

Question 140.
Is Latha right or wrong?
Answer:
Yes.

Question 141.
Which concept is used from your text-book to support Latha?
Answer:
Mensuration
A toy is in the form of a cone mounted on a hemisphere. The radius of the base and the height of the cone are 7 Cm and 8 cm respectively.

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 142.
What is the common measure in the toy of two situations?
Answer:
Radius of hemisphere = Radius of cone.

Question 143.
Find the slant height of cone.
Answer:
l = \(\sqrt{113} \mathrm{~cm}\)cm

Question 144.
For finding surface area of the toy, what are required?
Answer:
C.S. A of cone and surface area of hemisphere.
An ice-cream cone full of ice-cream having radius 5 cm and height 10 cm.
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 13

Question 145.
Write the combinations of given solid figure.
Answer:
Cone + hemisphere

Question 146.
What are the radii of cone and hemisphere?
Answer:
Hemisphere radius = 5 cm and cone radius = 5 cm

Question 147.
How much the volume of ice-cream contained in conical part?
Answer:
V = 130.95 cm3

Question 148.
How much the volume of ice-cream contained in hemisphere part?
261.90 cm3

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 149.
For figure shown, match the column.
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 14
Answer:
A – (ii), B – (i), C – (iii), D – (iv)

Question 150.
For a wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in fig. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm.
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 15
Answer:
A – (iii), B – (iv), C – (ii), D – (i)

Question 151.
From a solid cylinder of height 2.4 cm and diameter 1.4 cm., a conical cavity of the same height and some diameter is followed out them match the column.
AP 10th Class Maths Bits Chapter 10 Mensuration with Answers 16
Answer:
A – (ii), B – (i), C – (iii), D – (iv)

Question 152.
The capacity of an oil drum is 10litres then what is its volume? (in cm3)
AP LModel Paper I
Answer:
10,000 cm3

Question 153.
Food grains are to be stored in containers of the same base length and height. Which type of containers are required less in number to store a fixed quantity of grains?
i) Right Circular Cylinder
ii) Cube
iii) Right Circular Cone
Answer:
ii) Cube

AP 10th Class Maths Bits Chapter 10 Mensuration with Answers

Question 154.
An open water tank is in the shape of a Cuboid with outer dimensions – length V units, breadth ‘y’ units and height ‘z’ units. If the thickness of the wall is ‘a’ units, express the inner dimensions.
Solution:
Inner Dimensions :
Length = x – a – a = x – 2a units
(both side wall thickness reduced).
Breadth = y – a – a = y – 2a units
(both side wall thickness reduced).
Height = z – a units (as open from top so only bottom thickness reduced)

Question 155.
Choose the correct answer satisfying the following statements.
Statement (A) : The ratio of volumes of cone and cylinder of same base and same height is 3 : 1 Statement (B) : The ratio of volumes of sphere and cone of same radius and same height is 2 : 1
i) Both A and B are true
ii) A is true, B is false
iii) A is false, B is true .
iv) Both A and B are false
Answer:
iv) Both A and B are false