Volume and Surface Area of Solid Figures
- 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 cm2. Which one of the following is correct ?
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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.Correct Option: A
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.
- 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. ?
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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 = 4394Correct Option: B
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
- 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. ?
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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 cm3Correct Option: B
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
- 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.
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Capacity of tank = = 50000 L = 50 m3 [∴ 1L = 1/1000 m3 ]
∴ Breadth = 50/(2.5 x 10) = 2 mCorrect Option: A
Capacity of tank = = 50000 L = 50 m3 [∴ 1L = 1/1000 m3 ]
∴ Breadth = 50/(2.5 x 10) = 2 m
- 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 ?
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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 brickCorrect Option: A
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
