# AP 10th Class Maths 12th Chapter Surface Areas and Volumes Bits

## Chapter 12 Surface Areas and Volumes Bits for 10th Class AP Board

Multiple Choice Questions (MCQs)

Question 1.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire
is ……………….. .
A) 36 m
B) 24 m
C) 26 cm
D) 34 cm
A) 36 m

Question 2.
A solid sphere of radius r is melted and cost into the shape of a solid cone of height r, the radius of the base of
the cone is ………………… .
A) r
B) 2r
C) 3r
D) 4r
B) 2r

Question 3.
The number of solid sphere, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height
45 cm and diameter 4 cm is …………………. .
A) 15
B) 10
C) 5
D) 3
C) 5

Question 4.
A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3 times the volume of the cone, then the height of the circular cylinder is ………………. .
A) $$\frac{3 h}{2}$$
B) $$\frac{2 h}{2}$$
C) 3h
D) 2h
D) 2h

Question 5.
The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is …………….. .
A) 136π cm2
B) 36π cm2
C) 120π cm2
D) 128π cm2
A) 136π cm2

Question 6.
The volume of two spheres are in the ratio 27 : 64. The ratio of their surface areas is ………………… .
A) 9 : 16
B) 16 : 9
C) 3 : 4
D) 4 : 3
A) 9 : 16

Question 7.
The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is ……………… .
A) 18 cm
B) 12 cm
C) 6 cm
D) 3 cm
C) 6 cm

Question 8.
A right triangle with sides 3 cm, 4 cm, and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is ……………. .
A) 12π cm3
B) 6π cm3
C) 3π cm3
D) 8π cm3
A) 12π cm3

Question 9.
The curved surface area of a cylinder is 264 m2 and its volume is 924 m3. The ratio of its diameter to its height is ……………. .
A) 3 : 7
B) 5 : 7
C) 7 : 3
D) 7 : 5
C) 7 : 3

Question 10.
The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is ……………… .
A) 1 : 5
B) 5 : 1
C) 1 : 4
D) 4 : 1
A) 1 : 5

Question 11.
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is ……………. .
A) 2 : 1
B) 5 : 1
C) 3 : 1
D) 4 : 1
D) 4 : 1

Question 12.
The radii of the ends of bucket 16 cm high are 20 cm and 18 cm. The curved surface area of the bucket is ……………… .
A) 3520 cm2
B) 1670 cm2
C) 1760 cm2
D) 980 cm2
C) 1760 cm2

Question 13.
A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by ……………. .
A) $$\frac{5}{4}$$ cm
B) $$\frac{9}{4}$$ cm
C) $$\frac{4}{5}$$ cm
D) $$\frac{7}{4}$$ cm
B) $$\frac{9}{4}$$ cm

Question 14.
The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5 cm then the height of the cone is ……………. .
A) 15 cm
B) 20 cm
C) 25 cm
D) 30 cm
A) 15 cm

Question 15.
A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m. The total area of the canvas required in m2 is …………….. .
A) 8920
B) 7430
C) 6785
D) 7920
D) 7920

Question 16.
A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones is …………….. .
A) 130
B) 162
C) 126
D) 150
C) 126

Question 17.
A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is ……………….. .
A) 8 cm
B) 6 cm
C) 4 cm
D) 2 cm
A) 8 cm

Question 18.
A solid piece of iron of dimensions 49 × 33 × 24 cm is moulded into a sphere. The radius of the sphere is …………….. .
A) 7 cm
B) 21 cm
C) 14 cm
D) 28 cm
B) 21 cm

Question 19.
Aditya wants to make a solid brick shape structure from 400 wooden cubes of unit volume each. If the sides of the solid brick have the ratio 1 : 2 : 3, then the maximum number of cubes, which can be used, will be ……………..
A) 483
B) 384
C) 325
D) 425
B) 384

Question 20.
A rectangular sheet paper 40 cm × 22 cm is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder is ……………. .
A) 9.5 cm
B) 7 cm
C) 3.5 cm
D) 4.5 cm
C) 3.5 cm

Fill in the blanks:

1. Ratio of lateral surface areas of two cylinders with equal height is _________ .
R : r

2. The volume of a cube with diagonal d is _________ .
$$\frac{d^3}{3 \sqrt{3}}$$ cm3

3. A cube is a special type of __________ .
cuboid

4. The volume of a solid is the measurement of the portion of the ________ occupied by it.
space

5. The volume of sphere of diameter is _________ .
$$\frac{\pi \mathrm{d}^3}{6}$$

6. The length of the diagonal of a cube that can be inscribed in a sphere of radius 7.5 cm is _________ .
15 cm

7. If the volume of a cube is 64 cm3 then its surface area is __________ .
96 cm2

8. The length of the diagonal of a cube that can be inscribed in a sphere of radius 7.5 cm is __________ .
3 units

9. The volume of a cylinder is 448 cm3 and height 7 cm. then its lateral surface area is __________ .
352 cm2

10. Cubes x, y! z having edges of 18 cm, 24 cm and 30 cm respectively are melted and moulded into a new cube A. Then the edge of the cube A. ________ .
36 cm

11. The diameter of hollow cone is equal to the diameter of a spherical ball. If the ball is placed at the base of the cone, then portion of the hall will be outside cone _________ .
50%

12. A sphere and a cube have equal surface areas, then the ratio of the diameter of the sphere to the edege of the cube is _________ .
√6 : √π

13. The diagram shows the parts of a right cylinder. The volume of a cylinder is ________ .
im
$$\frac{50}{\pi}$$ cm3

14. If the perimeter of one face of a cube is 20 cm then its surface area is _________ .
150 cm2

15. The total surface area of a solid cylinder of radius r and height h is _________ .
2πr (h + r)

16. If the diameter of a garden roller is 1.4 m and 2 m long, then the area will it cover in 5 revolutions