Discussion
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- Question
- The base of a cone and a cylinder have the same radius 6 cm. They have also the same height 8 cm. The ratio of the curved surface of the cylinder to that of the cone is?
Options- A. 4 : 3
- B. 5 : 3
- C. 8 : 5
- D. 8 : 3
- Correct Answer
- 8 : 5
ExplanationRatio of curved surface area of cylinder and cone = [2?rh] / [?r?h2 + r2]
= [2 x 6 x 8] / [6 x ?62 + 82]
= 96/(6 x 10) = 96/60 = 8/5 = 8 : 5 - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is?
Options- A. 7500
- B. 13500
- C. 3500
- D. 4500 Discuss
- 7. How many spherical bullets can be made out of a solid cube whose edge measures 44 cm, each bullet being 4 cm in diameter?
Options- A. 2550
- B. 2541
- C. 2500
- D. 2575 Discuss
- 8. The volumes of a sphere and a right circular cylinder having the same radius are equal. The ratio of the diameter of the sphere to the height of the cylinder is?
Options- A. 1 : 2
- B. 2 : 1
- C. 2 : 3
- D. 3 : 2 Discuss
- 9. The radius of a sphere and a right circular cylinder are equal and their curved surface areas are also equal. The ratio of their volumes is?
Options- A. 3 : 4
- B. 2 : 3
- C. 3 : 2
- D. 4 : 3 Discuss
- 10. The volume of a cuboid is twice the volume of a cube. If the dimensions of total cuboid are 9 cm, 8 cm and 6 cm, then total surface area of the cube will be?
Options- A. 213 sq cm
- B. 216 sq cm
- C. 218 sq cm
- D. 219 sq cm Discuss
Volume and Surface Area problems
Search Results
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.
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
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
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
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%
Correct Answer: 13500
Explanation:
Let required number of coins be n, Then,
n x 1/3 x ? (1/10)2 x 1 = ? x (3)2 x 5
? n = 9 x 5 x 3 x 100 = 13500
Correct Answer: 2541
Explanation:
Volume of 1 bullet = 4/3?(2)3 = (32/3 x 22/7) cm3
Volume of the cube = (44)3
? Number of bullets = Volume of solid/Volume of 1 bullet
= (44)3 x 3 x 7 / 32 x 22 = 2541
Correct Answer: 3 : 2
Explanation:
Let r = Radius of cylinder = Radius of sphere, h = Height of the cylinder.
According to the question.
4/3?r3 = ?r2h
? h = 4r/3
? 4r = 3h
? 2r = 3/2h
? 2r/h = 3/2
? Required ration = 3 : 2
Correct Answer: 2 : 3
Explanation:
Given, 4?r2 = 2?rh
? h = 2r
Now, required ratio
= 4/3?r3 : ?r2h
= 4r : 3h
= 4r : 6r [ ? h = 2r]
= 2 : 3
Correct Answer: 216 sq cm
Explanation:
Volume of the cuboid = 9 x 8 x 6 = 432 cm3
Volume of the cube = 1/2 x 432 = 216 cm3
? Each side of cube = ?216 = 6 cm
Total surface area of the cube = 6 x (Side)2 = 6 x 62
= 6 x 36 = 216 sq cm
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