Volume and Surface Area problems
- 1. A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are ? 70. What is the rate of painting per square centimetre?
Options- A. ? 0.7 per cm2
- B. ? 0.5 per cm2
- C. ? 0.1 per cm2
- D. ? 0.2 per cm2 Discuss
Correct Answer: ? 0.1 per cm2
Explanation:
As the box is painted from inside, the dimensions of the box from inside are
Length = (21 - 05 - 05) = 20 cm
Breadth = (11 - 05 - 05) = 10 cm and height = (6 - 05) = 5.5
Total number of faced to be painted = 4 walls + One base
The dimensions of two of the walls = 2 x (10 x 5.5)
The dimensions of the remaining two = 2 x (20 x 5.5) and that of the base = (20 x 10 ) and so the total area to be pained = 2 x (10 x 5.5) + 2 x (20 x 5.5) + (20 x 10 ) = 530cm3
Since, the total expenses of painting this area is ?70, the rate of painting
= 70/530 = 0.13 = ? 0.1 per cm3 (approx)
- 2. A wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangular boxes of dimensions 8 cm x 7 cm x 6 cm. The maximum number of boxes that can be carried in 1 wooden box is?
Options- A. 1200000
- B. 1000000
- C. 9800000
- D. 7500000 Discuss
Correct Answer: 1000000
Explanation:
Number of boxes = (Volumes of wooden box in cm3) / (Volume of 1 small box)
= (800 x 700 x 600) / (8 x 7 x 6) = 1000000
- 3. If the length breadth and the height of cuboid are in the ratio 6 :5 : 4 and if the total surface area is 33300 cm 2, then the length, breadth and height in cm. are respectively?
Options- A. 90, 85, 60
- B. 85, 75, 60
- C. 90, 75, 70
- D. 90, 75, 60 Discuss
Correct Answer: 90, 75, 60
Explanation:
Let length = 6k, breadth = 5k and height = 4k in cm
? 2(6k x 5k + 5k x 4k + 6k x 4k) = 33300
? 148k2 = 33300
? k2 = 33300/148 = 225
? k = 15
? Length = 90 cm, Breadth = 75 cm, Height = 60 cm
- 4. If the length of diagonal of a cube is 8? 3 cm, then its surface area is?
Options- A. 512 cm2
- B. 384 cm2
- C. 192 cm2
- D. 786 cm2 Discuss
Correct Answer: 384 cm2
Explanation:
? ?3a = 8?3
? a = 8
? Surface area = 6a2
= (6 x 8 x 8) cm2
= 384 cm2
- 5. The length of longer pole that can be placed on the floor of a room is 10 m and the length of the longest pole that can be placed in the room is 10? 2m. The height of the room is?
Options- A. 6 m
- B. 7.5 m
- C. 8 m
- D. 10 m Discuss
Correct Answer: 10 m
Explanation:
? l2 + b2 = (10)2 = 100
And l2 + b2 + h2 = (10?300)2 = 200
? h2 = (200 - 100) = 100
? h = 10 m
- 6. The length of diagonal of a cube is (14 x ? 3) cm. The volume of the cube is?
Options- A. 2744?3 cm3
- B. 2744 cm3
- C. 588 cm3
- D. 3528 cm3 Discuss
Correct Answer: 2744 cm3
Explanation:
? ?3 a = 14 x ?3
? a = 14
? Volume of the cube = (14 x 14 x 14)cm3
= 2744 cm3
- 7. The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm x 6 cm x 2 cm is?
Options- A. 2 ?13 cm
- B. 2 ?14 cm
- C. 2 ?26 cm
- D. 10 ?2 cm Discuss
Correct Answer: 2 ?26 cm
Explanation:
Length of pencil = ? [(8)2 + (6)2 + (2)2] cm
= ?104 cm
= 2?26
- 8. A river 2 m deep and 45 m wide is running at the rate of 3 km/hr. The amount of water that runs into the per minute is?
Options- A. 4500 m3
- B. 27000 m3
- C. 3000 m3
- D. 2100 m3 Discuss
Correct Answer: 4500 m3
Explanation:
Speed per min = (3 x 1000)/60 m = 50 m
Volume of water running per min. = (45 x 2 x 50) m2
= 4500 m3
- 9. Bricks are worth Rs. 750 per 1000 and their length, breadth and height 25 cm, 12.5 cm and 7.5 cm respectively. The cost of bricks required to build a wall 200 m long, 1.8 m high and 37.5 cm thick is?
Options- A. Rs. 42, 600
- B. Rs. 43, 200
- C. Rs. 40, 750
- D. Rs. 41, 860 Discuss
Correct Answer: Rs. 43, 200
Explanation:
Number of bricks required = Volume of wall in cm3 / Volume of 1 brick
= (200 x 100 x 1.8 x 100 x 37.5)/(25 x 12.5 x 7.5)
= 57, 600
? Required cost = Rs. (750 x 57600)/1000
= Rs. 43, 200
- 10. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between the surface area of two solids is?
Options- A. 284 cm2
- B. 286 cm2
- C. 296 cm2
- D. 300 cm2 Discuss
Correct Answer: 286 cm2
Explanation:
Volume of cube formed = 216 cm3
? Edge of the cube = (6 x 6 x 6)1/3 = 6 cm
Surface area of original metal sheet = 2(27 x 8 + 8 x 1 + 27 x 1) cm2 = 502 cm2
Surface area of the cube formed = [6 x (6)2] cm2 = 216 cm2
? Required difference in area of two solids = (502 - 216) cm2
= 286 cm2
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