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 cm^{2}

B) 224 cm^{2}

C) 448 cm^{2}

D) 288 cm^{2}

Answer:

C) 448 cm^{2}

Question 2.

Lateral surface area of a cube whose edge is 3.5 cm is

A) 12.25 cm^{2}

B) 42.875 cm^{2}

C) 73.5 cm^{2}

D) 49 cm^{2}

Answer:

D) 49 cm^{2}

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 cm^{3}

B) 216 cm^{3}

C) 512 cm^{3}

D) 384 cm^{3}

Answer:

C) 512 cm^{3}

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 cm^{3}

B) 48 cm^{3}

C) 72 cm^{3}

D) 60 cm^{3}

Answer:

C) 72 cm^{3}

Question 7.

The volume of a square pyramid whose base area is 16 cm and height 8 cm is

A) 128 cm^{3}

B) 144 cm^{3}

C) 64 cm^{3}

D) 256 cm^{3}

Answer:

A) 128 cm^{3}

Question 8.

The volume of a cube is 729 cm^{3} ,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 cm^{3}, 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 cm^{3}

B) 60 cm^{3}

C) 360 cm^{3}

D) can’t be determined

Answer:

A) 180 cm^{3}

Question 12.

The C.S.A. of a right circular cylinder whose r = 21 cm and h = 7 cm

A) 924 cm^{2}

B) 6468 cm^{2}

C) 9702 cm

D) 67914 cm^{2}

Answer:

A) 924 cm^{2}

Question 13.

Total surface area of a cylinder whose diameter is 14 cm and height 7 cm

A) 1848 cm^{2}

B) 1884 cm^{2}

C) 1488 cm^{2}

D) 392 cm^{2}

Answer:

A) 1848 cm^{2}

Question 14.

Volume of a cylinder when d = 7 cm and h = 3 cm

A) 118 cm^{3}

B) 115.5 cm^{3}

C) 155.5 cm^{3}

D) 808.5 cm^{3}

Answer:

B) 115.5 cm^{3}

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 cm^{2}

B) 192 cm^{2}

C) 48 cm^{2}

D) 576 cm^{2}

Answer:

C) 48 cm^{2}

Question 16.

C.S.A of a cone is

A) \(\frac{1}{3}\)πr^{2}h

B) πr^{2}l

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 cm^{2}

B) 24 cm^{2}

C) 54 cm^{2}

D) 44 cm^{2}

Answer:

D) 44 cm^{2}

Question 19.

The T.S.A of a cone whose d = 14 cm, h = 24 cm

A) 504 cm^{2}

B) 3696 cm^{2}

C) 704 cm^{2}

D) 528 cm^{2}

Answer:

C) 704 cm^{2}

Question 20.

Volume of a cone whose base radius is 4.2 cm and height is 4 cm

A) 73.92 cm^{2}

B) 52.8 cm^{2}

C) 48.6 cm^{2}

D) 40.8 cm^{2}

Answer:

A) 73.92 cm^{2}

Question 21.

Surface area of a sphere is

A) 4πr^{2}

B) 3πr^{2}

C) 2πr^{2}

D) 5πr^{2}

Answer:

A) 4πr^{2}

Question 22.

Volume of a sphere is

A) \(\frac{2}{3}\)πr^{3}

B) \(\frac{4}{3}\)πr^{3}

C) πr^{3}

D) \(\frac{5}{6}\)πr^{3}

Answer:

B) \(\frac{4}{3}\)πr^{3}

Question 23.

Surface area of a hemisphere is

A) 2πr^{2}

B) 3πr^{2}

C) 4πr^{2}

D) πr^{2}

Answer:

B) 3πr^{2}

Question 24.

The volume of a sphere whose radius is 7 cm

A) 1437.3 cm^{3}

B) 4337 cm^{3}

C) 2588 cm^{3}

D) 4678 cm^{3}

Answer:

A) 1437.3 cm^{3}

Question 25.

The total surface area of a hemisphere whose radius is 14 cm

A) 2156 cm^{2}

B) 616 cm^{2}

C) 1258 cm^{2}

D) 1848 cm^{2}

Answer:

D) 1848 cm^{2}

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 cm^{2}

B) 210 cm^{2}

C) 426 cm^{2}

D) 213 cm^{2}

Answer:

B) 210 cm^{2}

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 cm^{3}

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 cm^{2}

B) 64 cm^{2}

C) 384 cm^{2}

D) 256 cm^{2}

Answer:

D) 256 cm^{2}

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) πr^{2}h

B) \(\frac{1}{3}\)πr^{2}h

C) πh (R^{2} – r^{2})

D) 3πr^{2}h

Answer:

B) \(\frac{1}{3}\)πr^{2}h

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) \(\frac{4}{3}\)πr^{3}

B) \(\frac{2}{3}\)πr^{3}

C) \(\frac{1}{3}\)πr^{2}h

D) πr^{2}h

Answer:

B) \(\frac{2}{3}\)πr^{3}

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 cm^{2}

B) √3 cm^{2}

C) 4 cm^{2}

D) 8 cm^{2}

Answer:

B) √3 cm^{2}

Question 46.

Volume of a pyramid whose base area is 18 cm^{2} and height 8 cm is

A) 48 cm^{3}

B) 64 cm^{3}

C) 72 cm^{3}

D) 96 cm3

Answer:

A) 48 cm^{3}

Question 47.

A regular square pyramid has its base edge 6 cm and height 5 cm. Then its volume is

A) 36 cm^{3}

B) 25 cm^{3}

C) 11 cm^{3}

D) 60 cm^{3}

Answer:

D) 60 cm^{3}

Question 48.

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

A) 220 cm^{3}

B) 1540 cm^{3}

C) 770 cm^{3}

D) 440 cm^{3}

Answer:

B) 1540 cm^{3}

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) πx^{2}y

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 cm^{2}

B) 46.2 cm^{2}

C) 73.5 cm^{2}

D) 7.35 cm^{2}

Answer:

A) 123.2 cm^{2}

Question 54.

Formula to find the slant height of a cone is

A) l = h^{2} + r^{2}

B) l^{2} = 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) 4πr^{2}

D) 2πr^{2}

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 cm^{2}, then it’s volume is

A) 8 cm^{3}

B) 27 cm^{3}

C) 64 cm^{3}

D) 125 cm^{3}

Answer:

C) 64 cm^{3}

Question 58.

If the radius of sphere is 14 cm then it’s surface area is

A) 1464 cm^{2}

B) 2464 cm^{2}

C) 3464 cm^{2}

D) 4464 cm^{2}

Answer:

B) 2464 cm^{2}

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) cm^{2}

B) 2π xy cm^{2}

C) π x^{2}y

D) 2π x^{2}y cm^{2}

Answer:

B) 2π xy cm^{2}

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 cm^{3}

B) 405 cm^{3}

C) 505 cm^{3}

D) 205 cm^{3}

Answer:

B) 405 cm^{3}

Question 66.

If Akshra formed a cuboid using all that cubes, then the total surface area of cuboid is

A) 177 cm^{2}

B) 354 cm^{2}

C) 405 cm^{2}

D) 144 cm^{2}

Answer:

C) 405 cm^{2}

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) 4πx^{3}

B) \(\frac{8 \pi}{3}\)x^{3}

C) \(\frac{32}{3}\)πx^{3}

D) \(\frac{4}{3}\)πx^{3}

Answer:

C) \(\frac{32}{3}\)πx^{3}

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 m^{3} 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 cm^{2}, 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 cm^{2}, then its volume is

A) 27 cm^{3}

B) 64 cm^{3}

C) 512 cm^{3}

D) 8 cm^{3}

Answer:

B) 64 cm^{3}

Question 78.

A hemispherical bowl has a radius of 3.5 cm, then its curved surface area is

A) 77 cm^{2}

B) \(\frac{231}{2}\)cm^{2}

C) \(\frac{539}{6}\)cm^{2}

D) \(\frac{77}{2}\)cm^{2}

Answer:

A) 77 cm^{2}

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) 3πr^{2}

b) πrl

c) \(\frac{4}{3}\)πr^{3}

d) πr^{2}h

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 m^{3} 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 cm^{2}, 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) πr^{2}

B) 2πr^{2}

C) 3πr^{2}

D) 4πr^{2}

Answer:

A) πr^{2}

Question 85.

The curved surface area of a cylinder having r = x cm, h = y cm is ……… an

A) 2πr (x + y)

B) πx^{2}y

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 cm^{2}

B) 65 cm^{2}

C) 32.5 cm^{2}

D) 46 cm^{2}

Answer:

B) 65 cm^{2}

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 cm^{2}

B) 12 cm^{2}

C) 16 cm^{2}

D) 28 cm^{2}

Answer:

D) 28 cm^{2}

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 cm^{2}

B) 102 cm^{2}

C) 56 cm^{2}

D) 153 cm^{2}

Answer:

A) 51 cm^{2}

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