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Question
The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 square centimetres. The volume of the solid, in cubic centimetres, is ______.
Options
192
384
480
2592
Solution
The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 square centimetres. The volume of the solid, in cubic centimetres, is 192.
Explanation:
Since, the solid has rectangular faces.
So, we have `l xx b = 16` ...(i)
`b xx h = 32` ...(ii)
`l xx h = 72` ...(iii)
Where `l, b` and `h` are the length, breadth and height respectively, of the solid.
On multiplying equations (i), (ii) and (iii), we get
`l xx b xx b xx h xx l xx h = 16 xx 32 xx 72`
⇒ `l^2 xx b^2 xx h^2 = 36864`
⇒ `(lbh)^2 = 36864`
∴ `lbh = 192`
Hence, the volume of the solid is 192 cu cm.
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