Volume and Surface Area problems
- 1. If the volume and surface are of a sphere are numerically the same then its radius is?
Options- A. 1 unit
- B. 2 unit
- C. 3 unit
- D. 4 unit Discuss
Correct Answer: 3 unit
Explanation:
4/3 ?r3 = 4?r2
? r = 3 units.
- 2. The volume of a sphere is 88/21 x (14) 3 cm 3. The curved surface of this sphere is?
Options- A. 2424 cm2
- B. 2446 cm2
- C. 2464 cm2
- D. 2484 cm2 Discuss
Correct Answer: 2464 cm2
Explanation:
? (4/3) x (22/7) x r3 = (88/21) x (14)3
? r = 14
? Curved surface = 4 x (22/7) x 14 x 14 cm2 = 2464 cm2
- 3. A cylinder and a cone have the same height and same radius of the base. The ratio between the volumes of the cylinder and the cone is?
Options- A. 1 : 3
- B. 3 : 1
- C. 1 : 2
- D. 2: 1 Discuss
Correct Answer: 3 : 1
Explanation:
Ratio of their volumes = [?r2h] / [(1/3)?r2h] = 3/1
= 3 : 1
- 4. The side of a cube measures 9 cm. What will be the diagonal of the cube (in cm)?
Options- A. 5?3
- B. 7?3
- C. 9?3
- D. 3?3 Discuss
Correct Answer: 9?3
Explanation:
Given, side of cube, a = 9
? Diagonal of cube = a?3 = 9?3
- 5. What will be the surface area of the sphere having 4 cm radius?
Options- A. 64? sq cm
- B. 69? sq cm
- C. 32? sq cm
- D. 35? sq cm Discuss
Correct Answer: 64? sq cm
Explanation:
Required surface area = 4?r2
= 4 x ? x 42 = 664? sq cm
- 6. A hemisphere has 3 cm radius. Calculate its volume.?
Options- A. 4/3 ? cm3
- B. 13 ? cm3
- C. 18? cm3
- D. 19/? cm3 Discuss
Correct Answer: 18? cm3
Explanation:
volume = (2/3)?r3
= (2/3) x ? x 33
= (2/3) x ? x 27
= 18? cm3
- 7. Find the total surface area of a pyramid having a slant height of 8 cm and a base which is a square of side 4 cm (in cm 2)?
Options- A. 80
- B. 64
- C. 72
- D. 84 Discuss
Correct Answer: 80
Explanation:
Total surface area of the pyramid
= [1/2(perimeter of the base) (Slant height) ] + Area of the base
= 1/2 (4) (4) (8) + 42 = 80 cm2
- 8. A sphere of radius r has the same volume as that of a cone with circular base of radius r. Find the height of the cone.?
Options- A. 2r
- B. r/3
- C. 4r
- D. (2/3)r Discuss
Correct Answer: 4r
Explanation:
Given that,
Volume of sphere = Volume of cone
? (4/3)?r3 = (1/3)?r2h
? 4r = h
- 9. A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 22 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the rose in level of the field will be?
Options- A. 0.299 cm
- B. 0.29 cm
- C. 2.98 cm
- D. 4.15 cm Discuss
Correct Answer: 2.98 cm
Explanation:
Earth dug out = (3 x 2 x 1.5 ) m3 = 9 m3
Area on which earth has been spread = (22 x 14 - 3 x 2 ) m2 = 302 m2
? Rise in level = Volume/Area = (9/302) m = (9 x 100/302) cm = 2.98 cm
- 10. Two cubes have volumes in the ratio 1: 27, The ratio of their surface areas is?
Options- A. 1 : 3
- B. 1 : 8
- C. 1 : 9
- D. 1 : 18 Discuss
Correct Answer: 1 : 9
Explanation:
Let the volume be x3 and 27x3
? Their edges are x and 3x
Now Ratio of their surface area = 6x2 : 54x2 = 1 : 9
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