The edges of a cuboid are in the ration 3:2:1 and it's surface area is $88 c m^{2}$ . Find the volume of a cuboid.

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Solution

Let the edge of a cuboid be $3 x, 2 x, x$ .

We know that, $S A = 2 (l \times b + b \times h + h \times l)$

Since,
$2 (3 x \times 2 x + 2 x \times x + x \times 3 x) = 88$

$6 x^{2} + 2 x^{2} + 3 x^{2} = 44$

$11 x^{2} = 44$

$x^{2} = 4$

$x = 2 c m$

So, the edges are $6 c m, 4 c m, 2 c m$

We know that the volume of the cuboid $= l \times b \times h$

Therefore,

Volume $= 6 \times 4 \times 2$

Volume $= 48 c m^{3}$

Hence, this is the answer.

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