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

Practice the AP 9th Class Maths Bits with Answers Chapter 10 Surface Areas and Volumes on a regular basis so that you can attempt exams with utmost confidence.

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

Choose the correct answer :

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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
C) 48 cm²

Question 16.
C.S.A of a cone is
A) \(\frac{1}{3}\)πr²h
B) πr²l
C) πrh
D) πrl
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
A) 73.92 cm²

Question 21.
Surface area of a sphere is
A) 4πr²
B) 3πr²
C) 2πr²
D) 5πr²
Answer:
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
Answer:
B) \(\frac{4}{3}\)πr³

Question 23.
Surface area of a hemisphere is
A) 2πr²
B) 3πr²
C) 4πr²
D) πr²
Answer:
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
Answer:
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
Answer:
D) 1848 cm²

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

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

Question 28.
The number of surfaces of a cuboid is
A) 4
B) 8
C) 6
D) 2
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
D) 256 cm²

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

Question 34.
Volume of a cone is
A) πr²h
B) \(\frac{1}{3}\)πr²h
C) πh (R² – r²)
D) 3πr²h
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
C) 1 : 4

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

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

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

Answer:
D) 15m

Question 65.
The volume of the structure built by Akshra
A) 305 cm³
B) 405 cm³
C) 505 cm³
D) 205 cm³
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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) \(\frac{7}{2}\)
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
C) 12√2

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

Question 90.
Area of the given figure is

A) 32 cm²
B) 12 cm²
C) 16 cm²
D) 28 cm²
Answer:
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
Answer:
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
Answer:
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°
Answer:
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
Answer:
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
Answer:
A) 51 cm²

Question 96.
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
Answer:
B) 10√2