## 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

Answer:

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

Answer:

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

Answer:

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

Answer:

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 cm^{2}

B) 36π cm^{2}

C) 120π cm^{2}

D) 128π cm^{2}

Answer:

A) 136π cm^{2}

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

Answer:

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

Answer:

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 cm^{3}

B) 6π cm^{3}

C) 3π cm^{3}

D) 8π cm^{3}

Answer:

A) 12π cm^{3}

Question 9.

The curved surface area of a cylinder is 264 m^{2} and its volume is 924 m^{3}. The ratio of its diameter to its height is ……………. .

A) 3 : 7

B) 5 : 7

C) 7 : 3

D) 7 : 5

Answer:

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

Answer:

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

Answer:

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 cm^{2}

B) 1670 cm^{2}

C) 1760 cm^{2}

D) 980 cm^{2}

Answer:

C) 1760 cm^{2}

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

Answer:

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

Answer:

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 m^{2} is …………….. .

A) 8920

B) 7430

C) 6785

D) 7920

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

C) 3.5 cm

Fill in the blanks:

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

Answer:

R : r

2. The volume of a cube with diagonal d is _________ .

Answer:

\(\frac{d^3}{3 \sqrt{3}}\) cm^{3}

3. A cube is a special type of __________ .

Answer:

cuboid

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

Answer:

space

5. The volume of sphere of diameter is _________ .

Answer:

\(\frac{\pi \mathrm{d}^3}{6}\)

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

Answer:

15 cm

7. If the volume of a cube is 64 cm^{3} then its surface area is __________ .

Answer:

96 cm^{2}

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

Answer:

3 units

9. The volume of a cylinder is 448 cm^{3} and height 7 cm. then its lateral surface area is __________ .

Answer:

352 cm^{2}

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. ________ .

Answer:

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 _________ .

Answer:

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 _________ .

Answer:

√6 : √π

13. The diagram shows the parts of a right cylinder. The volume of a cylinder is ________ .

im

Answer:

\(\frac{50}{\pi}\) cm^{3}

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

Answer:

150 cm^{2}

15. The total surface area of a solid cylinder of radius r and height h is _________ .

Answer:

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

Answer:

44 cm^{2}

17. A slab of ice length, breadth and height are 8 inches, 11 inches and 2 inches was melted and resolidified in the form of a rod of 8 inches diameter. Then the length of the rod in inches ________ .

Answer:

3.5 inches

18. 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is __________ .

Answer:

4 cm