Volume and Surface Area problems
- 1. A hemisphere has 28 cm diameter. Find its curved surface area.?
Options- A. 1232 sq cm
- B. 1236 sq cm
- C. 1238 sq cm
- D. 1233 sq cm Discuss
Correct Answer: 1232 sq cm
Explanation:
Curved surface area = 2?r2
= 2? x 14 x 14 = 2 x (22/7) x 14 x 14
= 2 x 22 x 2 x 14
= 88 x 14
= 1232 sq cm
- 2. What will be the difference between total surface area and curved surface area of a hemisphere having 2 cm diameter?
Options- A. 2? sq cm
- B. 3? sq cm
- C. ? sq cm
- D. 4? sq cm Discuss
Correct Answer: ? sq cm
Explanation:
Given,
Diameter = 2 cm
? r = 1 cm
Now, Total surface area of hemisphere = 3?r2
and curved surface area = 2?r2
Required difference = 3?r2 - 2?r2 = ?r2
= ? x 12 = ? sq cm
- 3. A metallic sphere of radius 12 cm is melted into three smaller spheres. If the radii of two smaller spheres are 6 cm and 8 cm, the radius of the third is?
Options- A. 14 cm
- B. 16 cm
- C. 10 cm
- D. 12 cm Discuss
Correct Answer: 10 cm
Explanation:
Let radius of the third sphere be r.
Then, 4/3 ? x (12)3 = 4/3 ? x (6)3 + 4/3? x (8)3 + 4/3 ?r3
? (12)3 = (6)3 + (8)3 + r3
? r3 = 1728 - 216 - 512
? r3 = 1000
? r = 10 cm
- 4. If the radius of a sphere is increased by 3%, then what percent increase takes place in surface area of the sphere?
Options- A. 6.09%
- B. 7%
- C. 5.06%
- D. 9% Discuss
Correct Answer: 6.09%
Explanation:
According to the formula
Percentage increase in surface area = [ 2x + x2/100]%
= [2 x 3 + (3)2/100]%
= [6 + 0.09]%
= 6.09%
- 5. If radius of a sphere is decreased by 24%, by what per cent does its surface area decrease?
Options- A. 44%
- B. 49%
- C. 42.24%
- D. 46.2% Discuss
Correct Answer: 42.24%
Explanation:
According to the formula,
Percentage decrease in surface area = [2 x (-24) + (-24) x (-24)/100]%
= [-48 + 5.76]% = - 42.24%
- 6. If the radius of a sphere is increased by 100%, by what per cent does its volume increase?
Options- A. 300%
- B. 900%
- C. 500%
- D. 700% Discuss
Correct Answer: 700%
Explanation:
Here, n = 100%
According to the formula
Percentage increase in volume = [(1 + n/100)3 - 1] x 100%
= [(1 + 100/100)3 - 1] x 100%
= [8 - 1] x 100% = 700%
- 7. Weight of a solid metallic sphere of radius 4 cm is 4 kg. The weight of a hollow sphere made with same metal, whose outer diameter is 16 cm and inner diameter is 12 cm, is?
Options- A. 20.5 kg
- B. 15.5 kg
- C. 16.5 kg
- D. 18.5 kg Discuss
Correct Answer: 18.5 kg
Explanation:
Volume of solid sphere of radius 4 cm = (4/3)?(4)3 cm3
Volume of hollow sphere = 4/3?[(8)3 - (6)3] cm3
? Weight of 4/3?(4)3 cm3 = 4 kg
= 4(512 - 216)/43 = 18.5 kg
- 8. A prism has the base a right angled triangle whose sides adjacent to the right angle are 10 cm and 12 cm long. The height of the prism is 20 cm. The density of the material of the prism is 6 g/cu cm. The weight of the prism is?
Options- A. 3.4 kg
- B. 4.8 kg
- C. 6.4 kg
- D. 7.2 kg Discuss
Correct Answer: 7.2 kg
Explanation:
Volume of prism = Area of base x Height
= (1/2) x 10 x 12 x 20
= 1200 cm2
? Weight of prism = 1200 x 6
= 7200 g
= 7.2 kg
- 9. The perimeter of the triangular base of a right prism is 60 cm and the sides of the base are in the ratio 5 : 12 : 13. Then, its volume will be (height of the prism being 60 cm).?
Options- A. 6000 cm3
- B. 6600 cm3
- C. 5400 cm3
- D. 9600 cm3 Discuss
Correct Answer: 6000 cm3
Explanation:
Let the sides of the base are 5k, 12k and 13k, respectively.
Given, perimeter of base = 60 cm
? 5k + 12k + 13k = 60
? k = 60/30 = 2
The sides of base are 10 cm, 24 cm 26 cm.
? Volume of prism = (1/2) x 10 x 24 x 50 = 6000 cm3
- 10. A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid?
Options- A. 1 : 1
- B. 1 : 3
- C. 3 : 1
- D. Cannot be determined Discuss
Correct Answer: 3 : 1
Explanation:
Volume of the prism = (Area of the base ) x (Height)
Volume of the pyramid = 1/3 (Area of the base ) x (Height)
Required ratio = [A x H] / [(1/3) x A x H]
Therefore, Ratio of the volumes of the prism and the pyramid = 3 : 1.
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