Volume and Surface Area problems
- 1. Internal length, breadth and height of a rectangular box are 10 cm, 8 cm and 6 cm, respectively. How many boxes are needed which can be packed in a cube whose volume is 6240 cu. cm.?
Options- A. 12
- B. 13
- C. 15
- D. 17 Discuss
Correct Answer: 13
Explanation:
Volume of rectangular box = 10 x 8 x 6 = 480 cm3
Volume of cubes = 6240 cm3
? Required boxes = Volume of cubes / Volume of rectangular box
= 6240/480 = 13
Hence, 13 boxes are needed.
- 2. A metal box measures 20 cm x 12 cm x 5 cm. Thickness of the metal is 1 cm. Find the volume of the metal required to make the box.?
Options- A. 550 cm3
- B. 656 cm3
- C. 660 cm3
- D. 475 cm3 Discuss
Correct Answer: 660 cm3
Explanation:
External volume = 20 x 12 x 5 = 1200 cm3
Internal volume = (20 - 2) x (12 - 2) x (5 - 2)
= 18 x 10 x 3 = 540 cm3
? Volume of the metal = External volume - Internal volume
= 1200 - 540 = 660 cm3
- 3. How many cubes of 3 cm edge be cut out of a cube of 18 cm edge?
Options- A. 63
- B. 432
- C. 216
- D. None of these Discuss
Correct Answer: 216
Explanation:
Let the number of cubes that can be cut from bigger cube = n. Then,
n x Volume of smaller cube = Volume of bigger cube
Edge of smaller cube = 3 cm
Edge of bigger cube = 18 cm
n x (3)3 = (18)3
? n = (18 x 18 x 18) / (3 x 3 x 3)
? n = 6 x 6 x 6 = 216 cubes
- 4. A cube has each edge 2 cm and a cuboid is 1 cm long, 2 cm wide and 3 cm high. The paint in a certain container is sufficient to paint an area equal to 54 cm 2. Which one of the following is correct?
Options- A. Both cube and cuboid can be painted
- B. Only cube can be painted
- C. Only cuboid can be painted
- D. Neither cube nor cuboid can be painted Discuss
Correct Answer: Both cube and cuboid can be painted
Explanation:
Surface area of cube which can be painted = 6(Side)2 = 6(2)2 = 24 cm2
Now, surface area of cuboid which can be painted
= 2(lb + bh + lh)
= 2(2 + 6 + 3) = 22 cm
Total surface area of both cube and cuboid
= 22 + 24 = 46 cm2 < 54 cm2
Therefore, both cube and cuboid can be painted.
- 5. The whole surface area of a rectangular block is 8788 sq cm. If length, breadth and height are in ratio of 4 : 3 : 2, then find the length.?
Options- A. 26 cm
- B. 52 cm
- C. 104 cm
- D. 13 cm Discuss
Correct Answer: 52 cm
Explanation:
Let length, breadth and height be 4k, 3k and 2k, respectively.
Whole surface area = 2(lb + bh + lh)
? (lb + bh + lh) = 8788/2 = 4394
? (4 x 3 + 3 x 2 + 2 x 4 ) k2 = 4394
? 26k2 = 4394
? k2 = 169
? k = 13
? Length = 4k = 4 x 13 = 52 cm
- 6. If the area of three advancement faces of a cuboidical box 120 sq cm, 72 sq cm and 60 sq cm, respectively, then find the volume of the box.?
Options- A. 820 cm3
- B. 720 cm3
- C. 750 cm3
- D. 750 cm3 Discuss
Correct Answer: 720 cm3
Explanation:
Given, lb = 120 sq cm., bh = 72 sq cm, lh = 60 sq cm.
? lb x bh x lh = 120 x 72 x 60
? (lbh)2 = 120 x 72 x 60
? lbh = ?120 x 72 x 60
= ?12 x 10 x 12 x 6 x 10 x 6
= 12 x 10 x 6 = 720 cm3
- 7. The capacity of a cuboid tank of water is 50000 L. Find the breadth of the tank, if its length and depth are 2.5 m and 10 m, respectively.
Options- A. 2 m
- B. 4 m
- C. 9 m
- D. 6 m Discuss
Correct Answer: 2 m
Explanation:
Capacity of tank = = 50000 L = 50 m3 [? 1L = 1/1000 m3 ]
? Breadth = 50/(2.5 x 10) = 2 m
- 8. The paint in certain container is sufficient to paint an area equal to dimensions 22.5 cm x 10 cm x 7.5 cm can be painted out of this container?
Options- A. 100
- B. 200
- C. 50
- D. 175 Discuss
Correct Answer: 100
Explanation:
Surface area of 1 brick
= 2 (lb + bh + lh)
= 2(22.5 x 10 + 10 x 7.5 + 7.5 x 22.5)
= 2(225 + 75 + 168.75)
= 2 x 468.75 = 937.50 cm2
= 93750/(100 x 100) = 0.09375 sq m
? Number of bricks = Total area/Surface area of 1 brick
= 9.375 / 0.09375 = 100
- 9. What are the dimensions (length, breadth and height, respectively) of a cuboid with volume 720 cu cm, surface area 484 sq cm and the area of the base 72 sq cm?
Options- A. 9, 8 and 10 cm
- B. 12, 6 and 10 cm
- C. 18, 4 and 10 cm
- D. 30, 2 and 12 cm Discuss
Correct Answer: 9, 8 and 10 cm
Explanation:
Volume of the cuboid = 720 cm3
Height of the cuboid = Volume of the cuboid / Base area of the cuboid
= 720 / 72 = 10 cm [By Hit Trail]
Surface area of the cuboid = 2 (lb + bh + hl)
= 2(9 x 8 + 8 x 10 + 10 x 9 )
= 2 (72 + 80 + 90)
= 2 x 242
= 484 cm2
? It is obvious that length, breadth and height of the cuboid is 9 cm, 8 cm and 10 cm.
- 10. The volume of a cube is numerically equal to sum of its edges. What is the total surface area in square units?
Options- A. 12
- B. 36
- C. 72
- D. 144 Discuss
Correct Answer: 72
Explanation:
Let the edge of a square be x. and sum of its edges = 12 x
Now, by condition, x3 = 12x
? x(x2 - 12) = 0
? Its total surface area = 6x2 = 6(12) = 72 sq units
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