# AP 9th Class Maths Bits Chapter 10 Surface Areas and Volumes with Answers

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## AP State Syllabus 9th Class Maths Bits 10th Lesson Surface Areas and Volumes with Answers

Question 1.
Surface area of a cuboid whose length, breadth and height are 10 cm, 8 cm and
8 cm is
A) 640 cm2
B) 224 cm2
C) 448 cm2
D) 288 cm2
C) 448 cm2

Question 2.
Lateral surface area of a cube whose edge is 3.5 cm is
A) 12.25 cm2
B) 42.875 cm2
C) 73.5 cm2
D) 49 cm2
D) 49 cm2

Question 3.
Volume of a right prism is
A) lbh
B) base perimeter × height
C) 2(lb + bh + lh)l + b + h
D) none
A) lbh

Question 4.
The volume of a cuboid whose side 8 cm is
A) 144 cm3
B) 216 cm3
C) 512 cm3
D) 384 cm3
C) 512 cm3

Question 5.
The volume of a pyramid is
A) $$\frac{1}{3}$$ × Area of base × height
B) $$\frac{1}{2}$$ × Area of base × height
C) Area of base × height
D) Perimeter of base × height
A) $$\frac{1}{3}$$ × Area of base × height

Question 6.
The volume of isosceles right angled triangular prism where the equal sides are 6 cm and 6 cm and height is 4 cm
A) 144 cm3
B) 48 cm3
C) 72 cm3
D) 60 cm3
C) 72 cm3

Question 7.
The volume of a square pyramid whose base area is 16 cm and height 8 cm is
A) 128 cm3
B) 144 cm3
C) 64 cm3
D) 256 cm3
A) 128 cm3

Question 8.
The volume of a cube is 729 cm3 ,then its side is
A) 27 cm
B) 9 cm
C) 7 cm
D) 36 cm
B) 9 cm

Question 9.
The volume, length and breadth of a cuboid are 60 cm3, 5 cm, 4 cm then its height is
A) 3 cm
B) 4 cm
C) 5 cm
D) 1.5 cm
A) 3 cm

Question 10.
If each dimension of a cuboid is increased by 4 times, then the total surface area becomes …………….. times the original area.
A) 4
B) 8
C) 12
D) 16
D) 16

Question 11.
The base of a prism is a triangle with sides 5 cm, 12 cm, 13 cm the volume of the prism if its height is 6 cm
A) 180 cm3
B) 60 cm3
C) 360 cm3
D) can’t be determined
A) 180 cm3

Question 12.
The C.S.A. of a right circular cylinder whose r = 21 cm and h = 7 cm
A) 924 cm2
B) 6468 cm2
C) 9702 cm
D) 67914 cm2
A) 924 cm2

Question 13.
Total surface area of a cylinder whose diameter is 14 cm and height 7 cm
A) 1848 cm2
B) 1884 cm2
C) 1488 cm2
D) 392 cm2
A) 1848 cm2

Question 14.
Volume of a cylinder when d = 7 cm and h = 3 cm
A) 118 cm3
B) 115.5 cm3
C) 155.5 cm3
D) 808.5 cm3
B) 115.5 cm3

Question 15.
A rectangular piece of length 12 cm and breadth 4 cm is folded to form a cylinder. Find its curved surface area.
A) 16 cm2
B) 192 cm2
C) 48 cm2
D) 576 cm2
C) 48 cm2

Question 16.
C.S.A of a cone is
A) $$\frac{1}{3}$$πr2h
B) πr2l
C) πrh
D) πrl
D) πrl

Question 17.
The radius of the base and height of a cone are 5 cm and 12 cm then its slant height
A) 17 cm
B) 7 cm
C) 13 cm
D) 6 cm
C) 13 cm

Question 18.
The C.S.A of a cone whose d = 7 cm, l = 4 cm
A) 34 cm2
B) 24 cm2
C) 54 cm2
D) 44 cm2
D) 44 cm2

Question 19.
The T.S.A of a cone whose d = 14 cm, h = 24 cm
A) 504 cm2
B) 3696 cm2
C) 704 cm2
D) 528 cm2
C) 704 cm2

Question 20.
Volume of a cone whose base radius is 4.2 cm and height is 4 cm
A) 73.92 cm2
B) 52.8 cm2
C) 48.6 cm2
D) 40.8 cm2
A) 73.92 cm2

Question 21.
Surface area of a sphere is
A) 4πr2
B) 3πr2
C) 2πr2
D) 5πr2
A) 4πr2

Question 22.
Volume of a sphere is
A) $$\frac{2}{3}$$πr3
B) $$\frac{4}{3}$$πr3
C) πr3
D) $$\frac{5}{6}$$πr3
B) $$\frac{4}{3}$$πr3

Question 23.
Surface area of a hemisphere is
A) 2πr2
B) 3πr2
C) 4πr2
D) πr2
B) 3πr2

Question 24.
The volume of a sphere whose radius is 7 cm
A) 1437.3 cm3
B) 4337 cm3
C) 2588 cm3
D) 4678 cm3
A) 1437.3 cm3

Question 25.
The total surface area of a hemisphere whose radius is 14 cm
A) 2156 cm2
B) 616 cm2
C) 1258 cm2
D) 1848 cm2
D) 1848 cm2

Question 26.
Which of the following is not a 3-D object?
A) Cone
B) Circle
C) Sphere
D) Cylinder
B) Circle

Question 27.
Which of the following is a 3-D object?
A) Rectangle
B) Circle
C) Square
D) Cylinder
D) Cylinder

Question 28.
The number of surfaces of a cuboid is
A) 4
B) 8
C) 6
D) 2
C) 6

Question 29.
The lateral surface area of a cuboid with dimensions 12 cm × 9 cm × 5 cm is
A) 540 cm2
B) 210 cm2
C) 426 cm2
D) 213 cm2
B) 210 cm2

Question 30.
The total length of all the edges of a cube of side 15 cm is
A) 225 cm
B) 120 cm
C) 180 cm
D) 60 cm
C) 180 cm

Question 31.
The edge of a cube whose volume is 1000 cm3
A) 10 cm
B) 100 cm
C) 50 cm
D) 20 cm
A) 10 cm

Question 32.
The lateral surface area of cube with side 8 cm is
A) 512 cm2
B) 64 cm2
C) 384 cm2
D) 256 cm2
D) 256 cm2

Question 33.
Total surface area of a cylinder is
A) 2πr (r + h)
B) πrl
C) πr (l + r)
D) 2πrh
A) 2πr (r + h)

Question 34.
Volume of a cone is
A) πr2h
B) $$\frac{1}{3}$$πr2h
C) πh (R2 – r2)
D) 3πr2h
B) $$\frac{1}{3}$$πr2h

Question 35.
A cone whose height and radius are 6 cm and 8 cm respectively. Then its
slant height is
A) 14 cm
B) 10 cm
C) 11 cm
D) 12 cm
B) 10 cm

Question 36.
The radius and slant height of a cone are 8 cm and 17 cm respectively. Then its height is
A) 15 cm
B) 12 cm
C) 9 cm
D) 16 cm
A) 15 cm

Question 37.
The height and slant height of a cone are 7 cm and 25 cm respectively. Then its radius is
A) 10 cm
B) 14 cm
C) 24 cm
D) 12.5 cm
C) 24 cm

Question 38.
Volume of a hemisphere is
A) $$\frac{4}{3}$$πr3
B) $$\frac{2}{3}$$πr3
C) $$\frac{1}{3}$$πr2h
D) πr2h
B) $$\frac{2}{3}$$πr3

Question 39.
The ratio of two spheres is 1 : 2, then the ratio of their surface areas is
A) 4 : 1
B) 1 : 8
C) 1 : 4
D) 8 : 1
C) 1 : 4

Question 40.
The horizontal cross – section of a cyl-inder is a
A) circle
B) triangle
C) rectangle
D) isosceles triangle
A) circle

Question 41.
The vertical cross – section of a cylinder is
A) square
B) rectangle
C) circle
D) sector
B) rectangle

Question 42.
The vertical cross – section of a cone is
A) triangle
B) circle
C) isosceles triangle
D) right angled triangle
C) isosceles triangle

Question 43.
When a cone is opened along its slant height, it gets the shape of a
A) sector
B) rectangle
C) square
D) equilateral triangle
A) sector

Question 44.
When a cylinder is opened along its height, it gets the shape of a
A) square
B) circle
C) rectangle
D) sphere
C) rectangle

Question 45.
Area of an equilateral triangle whose side is 2 cm is
A) 2√3 cm2
B) √3 cm2
C) 4 cm2
D) 8 cm2
B) √3 cm2

Question 46.
Volume of a pyramid whose base area is 18 cm2 and height 8 cm is
A) 48 cm3
B) 64 cm3
C) 72 cm3
D) 96 cm3
A) 48 cm3

Question 47.
A regular square pyramid has its base edge 6 cm and height 5 cm. Then its volume is
A) 36 cm3
B) 25 cm3
C) 11 cm3
D) 60 cm3
D) 60 cm3

Question 48.
Volume of the cylinder formed by a sheet as shown in the given figure.

A) 220 cm3
B) 1540 cm3
C) 770 cm3
D) 440 cm3
B) 1540 cm3

Question 49.
How does the total surface area of a box changed if each dimension is doubled?
A) T.S.A. of the box will become 4 times of original area.
B) T.S.A. of the box will become 3 times of original area.
C) T.S.A. of the box will become 6 times of original area.
D) T.S.A. of the box will become 8 times of original area.
A) T.S.A. of the box will become 4 times of original area.

Question 50.
A rectangle of length 44 cm is folded along with its breadth and formed a cylinder. Then the radius of the cylinder (cms) is
A) 44
B) 22
C) 11
D) 7
D) 7

Question 51.
Find curved surface area of a cylinder having r = x cm and h = y cm.
A) 2πx (x + y)
B) πx2y
C) πxy
D) 2πxy
D) 2πxy

Question 52.
The ratio of volumes of cylinder and cone having same radii and heights is
A) 1 : 2
B) 1 : 3
C) 3 : 1
D) 2 : 1
C) 3 : 1

Question 53.
Total surface area of the cylinder whose radius is 3.5 cm and height 2.1 cm.
A) 123.2 cm2
B) 46.2 cm2
C) 73.5 cm2
D) 7.35 cm2
A) 123.2 cm2

Question 54.
Formula to find the slant height of a cone is
A) l = h2 + r2
B) l2 = h + r
C) l = $$\sqrt{h^{2}+r^{2}}$$
D) l = h + r
C) l = $$\sqrt{h^{2}+r^{2}}$$

Question 55.
Surface area of a sphere whose radius is 1 unit.
A) 2π
B) 4π
C) 4πr2
D) 2πr2
B) 4π

Question 56.
A cone and cylinder have equal bases and heights. Their volumes in the ratio of
A) 1 : 3
B) 3 : 1
C) 2 : 3
D) 3 : 2
A) 1 : 3

Question 57.
The total surface area of cube is 96 cm2, then it’s volume is
A) 8 cm3
B) 27 cm3
C) 64 cm3
D) 125 cm3
C) 64 cm3

Question 58.
If the radius of sphere is 14 cm then it’s surface area is
A) 1464 cm2
B) 2464 cm2
C) 3464 cm2
D) 4464 cm2
B) 2464 cm2

Question 59.
If the radius and height of a cylinder is x cm and y cm respectively, then the curved surface area of cylinder.
A) 2πx (x + y) cm2
B) 2π xy cm2
C) π x2y
D) 2π x2y cm2
B) 2π xy cm2

Question 60.
The height of a cone is 12 cm. and its radius is 5 cm. then the slant height of cone is in cm.
A) 13
B) 17
C) 7
D) 12
A) 13

Question 61.
If the radius of a cylinder doubled, keeping its lateral surface area the same then its height is……………….
A) Increased by 50%
B) Increased by 100%
C) Decreased by 50%
D) Decreased by 100%
C) Decreased by 50%

Question 62.
Base of a coloured flag which is in the shape of triangle is 2 + √2 units and height is 2 – √2 units. Then the area of flag in square units.
A) 2
B) $$\frac{1}{2}$$
C) 1
D) 4
C) 1

Question 63.
In a cylinder, if radius is halved and height is doubled, then volume will be
A) Doubled
B) Halved
C) Four times
D) Same
B) Halved

Question 64.
The length of the longest flag pole that can be put in a store room of dimensions 10m × 10m × 5m is
A) 16m
B) 10m
C) 12m
D) 15m
Akshra playing with building blocks, which are of the shape of cubes, has built a structure as shown in given figure. If the edge of each cube is 3 cm, then answer the following questions from 10 to 14 :

D) 15m

Question 65.
The volume of the structure built by Akshra
A) 305 cm3
B) 405 cm3
C) 505 cm3
D) 205 cm3
B) 405 cm3

Question 66.
If Akshra formed a cuboid using all that cubes, then the total surface area of cuboid is
A) 177 cm2
B) 354 cm2
C) 405 cm2
D) 144 cm2
C) 405 cm2

Question 67.
Minimum number of small cubes further more required to form a cube
A) 12
B) 36
C) 48
D) 8
D) 8

Question 68.
If the ratio of volumes of two cubes is 8 : 27, then ratio of their total surface areas is
A) 2 : 3
B) 3 : 2
C) 3 : 1
D) 4 : 9
D) 4 : 9

Question 69.
The radius of the sphere is 2x, then its volume will be
A) 4πx3
B) $$\frac{8 \pi}{3}$$x3
C) $$\frac{32}{3}$$πx3
D) $$\frac{4}{3}$$πx3
C) $$\frac{32}{3}$$πx3

Question 70.
A pyramid is a three dimensional figure the base of which is
A) Only a square
B) Only a rectangle
C) Any polygon
D) Only a triangle
B) Only a rectangle

Question 71.
The steps from solids to points are
A) solids – lines – surface – points
B) lines – points – surface – solids
C) lines – surface – points – solids
D) solids – surface – lines – points
D) solids – surface – lines – points

Question 72.
A one side open cylindrical drum has inner radius 28 cm and height 2.1 m. then how much water store in the drum in litres?

(Hint : 1000 cubic cm = 1 litre)
A) 517.44
B) 51.744
C) 51744
D) 5174.40
D) 5174.40

Question 73.
On a particular day, the rainfall recorded in a terrace of dimensions 6 m and 5 m is 15 cm. The quantity of water collected in terrace is
A) 450 litres
B) 3000 litres
C) 4500 litres
D) 300 litres
A) 450 litres

Question 74.
The cost of construction of a wall 8 m long, 4 m height and 20 cm thick at the rate ₹ 25 per m3 is
A) ₹ 80
B) ₹ 160
C) ₹ 320
D) ₹ 16
B) ₹ 160

Question 75.
Which of the following is the solid combination of cylinder and cone ?
A) Capsule
B) Ice cream
C) Rocket
D) Top
C) Rocket

Question 76.
If the surface area of sphere is 154 cm2, then its radius in cms.
A) 7
B) 14
C) 21
D) $$\frac{7}{2}$$
B) 14

Question 77.
The total surface area of a cube is 96 cm2, then its volume is
A) 27 cm3
B) 64 cm3
C) 512 cm3
D) 8 cm3
B) 64 cm3

Question 78.
A hemispherical bowl has a radius of 3.5 cm, then its curved surface area is
A) 77 cm2
B) $$\frac{231}{2}$$cm2
C) $$\frac{539}{6}$$cm2
D) $$\frac{77}{2}$$cm2
A) 77 cm2

Question 79.
If the surface area of sphere is 616 cm2, then its radius is
A) 3.5 cm
B) 7 cm
C) 14 cm
D) 21 cm
B) 7 cm

Question 80.
In a cylinder, if radius is halved and height is doubled, then the volume will be
A) Same
B) Doubled
C) Halved
D) Four times
C) Halved

Question 81.
Match the following group A to B. Choose correct.
Group – A
1) Volume of the Sphere
2) Volume of the cylinder
3) CSA of cone
4) Total surface area of Hemisphere

Group – B
a) 3πr2
b) πrl
c) $$\frac{4}{3}$$πr3
d) πr2h
A) 1 – a, 2 – b, 3 – d, 4 – c
B) 1 – b, 2 – c, 3 – a, 4 – d
C) 1 – c, 2 – d, 3 – b, 4 – a
D) 1 – d, 2 – a, 3 – c, 4 – b
C) 1 – c, 2 – d, 3 – b, 4 – a

Question 82.
The cost of construction a wall whose dimensions are 8 m × 4 m × 20 cm at the rate of Rs. 25 per m3 is
A) Rs. 16
B) Rs. 80
C) Rs. 160
D) Rs. 320
C) Rs. 160

Question 83.
If the area of the equilateral triangle is 8√3 cm2, then its perimeter is in cms
A) 64
B) 32
C) 12√2
D) 4√2
C) 12√2

Question 84.
Which of the following represents the flat surface area of hemisphere ?
A) πr2
B) 2πr2
C) 3πr2
D) 4πr2
A) πr2

Question 85.
The curved surface area of a cylinder having r = x cm, h = y cm is ……… an
A) 2πr (x + y)
B) πx2y
C) πxy
D) 2πxy
D) 2πxy

Question 86.
The ratio of volumes of cylinder and cone having same radii and heights
A) 1 : 3
B) 3 : 1
C) 1 : 2
D) 2 : 1
B) 3 : 1

Question 87.
In a Rhombus the lengths of two diagonals are 10 cm and 13 cm then it’s area is……………………
A) 130 cm2
B) 65 cm2
C) 32.5 cm2
D) 46 cm2
B) 65 cm2

Question 88.
In this figure Area of the parallelogram PQRS is…………………

A) PQ × SM
B) RS × KQ
C) PS × QN
D) All
A) PQ × SM

Question 89.
A designer wanted to make a design with Iron rod. He has a rod of length 68 cm. He can do a rhombus of diagonals 16 cm, 30 cm and also a square. Which is a better option to cover more area with the given length?
A) Always both square & Rhombus
B) Square only
C) Rhombus only
D) Sometimes square and sometimes rhombus
D) Sometimes square and sometimes rhombus
B) Square only

Question 90.
Area of the given figure is

A) 32 cm2
B) 12 cm2
C) 16 cm2
D) 28 cm2
D) 28 cm2

Question 91.
≅ ABCD as shown in the figure is a field of a farmer. He sold ΔABX and ΔDCY to tally for ₹1.5 lakh in order to make it as a rectangular field AXYD. If he sells his total field, he might have get

A) ₹ 6 lakh
B) ₹ 1.5 lakh
C) ₹ 3 lakh
D) ₹ 45 lakh
C) ₹ 3 lakh

Question 92.
A toy rocket is like a cone exactly mounted on a cylinder the vertical cross-section of the toy is
A) Hexagon
B) Parallelogram
C) Rhombus
D) Trapezium
A) Hexagon

Question 93.
In a cyclic quadrilateral one set of opposite angles are in the ratio of 2 : 3, then the angles are
A) 40° 60°
B) 60°, 90°
C) 90°, 135°
D) 72° , 108°
D) 72° , 108°

Question 94.
From a metal sheet which is in the shape of a circle a biggest square with 10 cm as side was taken. Then the radius of the circle is (in ems)
A) 5√2
B) 10√2
C) 5
D) 7.5
B) 10√2

Question 95.
If the diagonal of a Rhombus are 12 cm. and 8.5 cm, then its area is
A) 51 cm2
B) 102 cm2
C) 56 cm2
D) 153 cm2