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

Answer 1

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.