Practice the AP 10th Class Maths Bits with Answers Chapter 10 Mensuration on a regular basis so that you can attempt exams with utmost confidence.

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

Question 1.

The total surface area of a cube is 54 cm^{2}, then find its side.

Answer:

3 cm

Explanation:

TSA = 6s^{2} = 54

⇒ side^{2} = 9 ⇒ side = 3 cm.

Question 2.

Base area of a regular cylinder is 154 cm^{2}, then find its radius.

Answer:

7 cm

Explanation:

πr^{2} = 154

⇒ r^{2} = 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:

Question 4.

Write a formula to find curved surface area of a hemisphere.

Answer:

2πr^{2}

Question 5.

How much the volume of a cube having 1 cm side ?

Answer:

1 cm^{3}

Question 6.

Ratio of volumes of two spheres is 8 : 27, then find ratio of their curved surface area.

Answer:

4 : 9

Explanation:

Question 7.

Football is in a model of …………..

Answer:

sphere

Question 8.

If the volume of a cube is 216 cm^{3}, then find its side.

Answer:

6 cm

Explanation:

S^{3} = 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 cm^{3}), whose total surface area is 216 cm^{2}.

Answer:

216

Explanation:

6S^{2} = 216

⇒ S^{2} = \(\frac{216}{6}\) = 36

⇒ S = \(\sqrt{36}\) = 6

∴ Volume = S^{3} = 6^{3} = 216

Question 12.

Write the name of a famous book writ-ten by ancient mathematician Aryabhatta.

Answer:

Aryabhatteeyam.

Question 13.

Which of the following vessel can be filled with more water (A, B are in cylindrical shape)?

Answer:

B)

Question 14.

Find the volume of right circular cylinder with radius 6 cm and height 7 cm.

Answer:

792 cm^{3}

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:

3πr^{2} = 7^{2} × 3 × π = 147π sq.m.

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:

\(\frac{1}{6}\) πa^{3}

Question 23.

If the total surface area of cube is 96 cm^{3}, then find side of cube.

Answer:

4 cm

Question 24.

Base area of the prism is 30 cm^{2} and its height is 10 cm. Then find the volume of the prism.

Answer:

300 cm^{3}

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 cm^{2}, then find its volume.

Answer:

64 cm^{3}

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:

πr^{2} + πrl

Question 29.

Find the volume of a hemisphere of radius 3.5 cm is …………… cm^{3}.

Answer:

89.83

Question 30.

In the above problem find TSA = ………………… cm^{2}.

Answer:

115.5

Question 31.

Write a combination of a shuttle cock.

Answer:

Hemisphere, frustum cone

Question 32.

The volume of cone is 462 cm^{3}, r = 7 cm, then find h is ……………… cm.

Answer:

9

Question 33.

10^{3} (cm)^{3} = ……………. litre.

Answer:

1

Question 34.

In l^{2} = h^{2} + r^{2}, h = 15, r = 8, then l = ………………

Answer:

17

Question 35.

The perimeter of an equilateral triangle is 60 cm, then find its area (in cm^{2}).

Answer:

173.2

Question 36.

Write the number of faces of a cuboid.

Answer:

8

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:

\(\frac{4}{3}\)πr^{3}

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:

3πr^{2}

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 cm^{3}

Question 46.

Find the volume of cone if r = 2 cm, h= 4 cm.

Answer:

\(\frac{16}{3}\)π cm^{3}

Explanation:

Volume of cone = \(\frac{1}{3}\) πr^{2}h

\(\frac{1}{3}\) × π × 4 × 4 = \(\frac{16}{3}\)π cm^{3}

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 …………….. cm^{3}.

Answer:

264

Explanation:

Volume of right circular cone V = \(\frac{1}{3}\) πr^{2}h

= \(\frac{1}{3}\) . π . 6^{2} . 7 = 264 cm^{3}.

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:

4πr^{2}

Question 53.

Total surface area of a cube is 216 cm^{2}, 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

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 (3R^{2} + r^{2})

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

= πr^{2}h : \(\frac{1}{3}\) πr^{2}h : \(\frac{2}{3}\) πr^{2}h

= \(\frac{1}{3}\) πr^{3} : \(\frac{2}{3}\) πr^{3} : πr^{3}

= 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)

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 cm^{2}

Question 61.

The volume of a vessel in the form of a right circular cylinder is 448π cm^{3} 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:

\(\frac{1}{6}\) πd^{2}

Question 63.

Write a formula to find total surface area of cylinder in ……………….. sq. units.

Answer:

2πrh+ 2πr^{2}

Question 64.

In a cylinder, r= 7 m, h=15 m, then find V.

Answer:

2310 m^{3}.

Question 65.

If the diagonals of a rhombus are 10 cm and 24 cm, then find area in ………………… cm^{2}.

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 cm^{2}

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 cm^{3}, then find its TSA (in cm^{2}).

Answer:

4158

Question 69.

r^{3} = 1728, then find ‘r’.

Answer:

12

Question 70.

In a cone, d = 14 cm, l = 10 cm, then find CSA = ……………….. cm^{2}.

Answer:

220

Question 71.

In the figure, P = …………………

Answer:

h^{2} + r^{2}

Question 72.

The surface area of a sphere is 616 sq.cm, then find its radius in …………. cm.

Answer:

7

Question 73.

In a hemisphere, r = 7 cm, then find CSA (in cm^{2})

Answer:

308

Question 74.

Write a formula to find volume of hollow cylinder.

Answer:

(πR^{2} – r^{2})

Question 75.

In a cube, a = 4 cm, then find TSA (in cm^{2}).

Answer:

90

Question 76.

In a cylinder, h=14 cm, V= 176 cm^{3}, r = …………….. cm.

Answer:

2

Question 77.

In a hemisphere, r = 1.75 cm, then find CSA (in cm^{2}).

Answer:

38.5

Question 78.

TSA of a cylinder is 1188 cm^{2}, h = 20 cm (in cm), then find its volume.

Answer:

3080

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 cm^{2}. If its height is 12 cm, then find its volume (in cm^{3}).

Answer:

314

Question 82.

Surface area of a sphere and cube are equal, then find the ratio of their volumes.

Answer:

√π : √6

Explanation:

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:

\(\frac{\mathrm{h}}{3}\) m^{2}

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 cm^{3}

Question 85.

The area of equilateral triangle is 36√3 cm^{2}, then find the perimeter (in etn).

Answer:

36

Explanation:

Area 36√3 cm^{2} ⇒ \(\frac{\sqrt{3} a^{2}}{4}\) = 36√3

⇒ a^{2} = 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 cm^{2}).

Answer:

13860

Question 87.

Write a formula to find area of equi¬lateral triangle of side ‘a’ units (in sq. units).

Answer:

\(\frac{\sqrt{3}}{4}\)a^{2}

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

Question 91.

Write a formula to find total surface area of a cube (in sq. units).

Answer:

6l^{2}

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:

\(\frac{2}{3}\)πr^{3}

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 cm^{3}, then find its edge.

Answer:

6

Question 97.

Write a formula find volume of cylinder (in cu. units).

Answer:

πr^{2}h

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:

a^{3}

Question 100.

The sphere of radius 2.1 cm, then find its volume (in cm^{3}).

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 m^{3}).

Answer:

\(\frac{5.2}{\sqrt{3}}\)

Explanation:

Applying Pythagoras theorem,

(2.5)^{2} = [a^{2} + (√2a)^{2}]

⇒ 6.25 = 3a^{2}

⇒ a^{2} = \(\frac{6.25}{3}\) ⇒ a = \(\frac{2.5}{\sqrt{3}}\) m^{3}

Volume of cube = a^{3}

\(\left(\frac{2.5}{\sqrt{3}}\right)^{3}\) = \(=\frac{15.625}{3 \sqrt{3}}=\frac{5.2}{\sqrt{3}}\) m^{3}

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 m^{3}).

Answer:

301.71

Question 104.

Perimeter of square is 20 cm, find then area (in cm^{2}).

Answer:

25

Question 105.

CSA of a cone is 4070 cm^{2} and its diameter is 70 cm, then find slant height.

Answer:

37

Question 106.

The volume of a cuboid is 3,36,000 cm^{3}. If its area is 5,600 cm^{2}, 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 cm^{3}

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

\(\frac{4}{3}\)πr^{3} = πr^{2}h

⇒ \(\frac{4}{3}\) × 3^{3} = h × 2^{2}

⇒ 4 × 9 = h × 4 ⇒ h = 9 cm

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

πr^{2}h = n × \(\frac{4}{3}\)πr^{3}

πr^{2}(8r) = n × \(\frac{4}{3}\)πr^{3}

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 = ……………….. cm^{3}

Answer:

\(\frac{3520}{7}\)

Question 115.

In a cone, (l + r)(l – r) = …………..

Answer:

h^{2}

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

Question 118.

Write a formula to find volume of cone, (in cu. units).

Answer:

\(\frac{1}{3}\)πr^{2}h

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 cm^{3}).

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 + h^{2} = 25

⇒ h^{2} = 25 – 16 = 9

⇒ h = 3 cm

Hence, (i) is the correct option.

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

= \(\frac{4}{3}\) πr^{3} and its surface area = 4πr^{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:

iv) Both A and B are false.

Explanation:

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 cm^{2}.

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 cm^{2}

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 = πr^{2}h 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:

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 = \(\frac{1}{3}\)πr^{2}h

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

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 cm^{2}.

Statement (B): Volume of a cone = \(\frac{1}{3}\)πr^{2}h

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 cm^{2}. Then its radius 6 cm.

Statement (B): Surface area of sphere = 4πr^{2}sq. 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 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 3πr^{2}sq. 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 cm^{2}.

Statement (B): If r be the radius and ‘h’ be the height of the cylinder, then total surface area= (2πrh + 2πr^{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:

A and B both are correct and B is the correct explanation of the A.

Total surface area = 2πrh × 2πr^{2}

= 2πrh × 2πr^{2}

= 2πr(h + r)

= 2 × \(\frac{22}{7}\) × 14 (30 + 14)

= 88 (44) = 3872 cm^{2}

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.

as V_{1} = V_{2}

∴ 4h_{1} = h_{2}

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 = 4πr^{2},

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.

Question 136.

Statement (A) : If the base area and height of a prism be 25 cm^{2} and 6 cm respectively, then its volume is 150 cm^{3}.

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 cm_{3}

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) m^{2}

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)m_{2}.

Question 138.

The slant height of the cone is

Answer:

13 m

Explanation:

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 m^{2}

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.

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.

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 cm^{3}

Question 148.

How much the volume of ice-cream contained in hemisphere part?

261.90 cm^{3}

Question 149.

For figure shown, match the column.

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.

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.

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 cm^{3})

AP LModel Paper I

Answer:

10,000 cm^{3}

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

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