Volume and Surface Area problems
- 1. 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 Discuss
Correct Answer: 8 : 5
Explanation:
Ratio 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
- 2. 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
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
- 3. 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
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
- 4. 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
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
- 5. 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
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
- 6. 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
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
- 7. Seven equal cubes each of side 5 cm are joined end-to-end. Find the surface area of the resulting cuboid .?
Options- A. 750 sq cm
- B. 1500 sq cm
- C. 2250 sq cm
- D. 700 sq cm Discuss
Correct Answer: 750 sq cm
Explanation:
Given, l = Length of the cuboid = 5 x 7 = 35 cm
h = Breadth of the cuboid = 5 cm
h = Height of the cuboid = 5 cm
? Surface area = 2(lb + bh + lh) = 2[35 x 5 + 5 x 5 + 35 x 5]
= 2[175 + 25 + 175]
= 2 x 375 = 750 sq cm
- 8. In a shower, 10 cm of rain falls, What will be the volume of water that falls on 1 hect area of ground?
Options- A. 500 cm3
- B. 650 cm3
- C. 1000 cm3
- D. 750 cm3 Discuss
Correct Answer: 1000 cm3
Explanation:
1 hec = 10000 m3
Volume of water = Base area x Height
= (10000 x 10)/100 = 1000 m3
- 9. Water flows at the rate of 10 m/min from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm?
Options- A. 51 min 12 s
- B. 52 min 1 s
- C. 48 min 15 s
- D. 55 min Discuss
Correct Answer: 51 min 12 s
Explanation:
Given, radius of pipe 5/2 x 10 = 5/20 cm [? 1 cm = 10 mm]
Height of pipe = 1000 cm
Radius of vessel = 20 cm and height = 24 cm
Volume of water flow in one minute from cylindrical pipe = ? (5/20)2 x 1000
= 125/2 ? cm3
and volume of conical vessel = 1/3 ?(20)2 x 24 = 3200? cm3
? Required time = (3200? x 2) / 125?
= 511/5 or 51 min 12 s
- 10. A cylindrical jar, whose base has a radius of 15 cm, is filled with water upto a height of 20 cm, A solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in water. Find the increase in the level of water (in cm).?
Options- A. 517/27
- B. 55/7
- C. 58/9
- D. 525/27 Discuss
Correct Answer: 525/27
Explanation:
Let level of water will be increased by h cm
? x (15)2 x h = (4/3)?(10)3
? h = [(4/3) x 10 x 10 x 10] / [15 x 15]
= 525/27 cm
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