The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 $m^{2}$ . The volume of cuboid is___ $m^{3}$

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Solution

The sides will be $x, 2 x, 3 x$

Total surface area $= 2 (x .2 x + 2 x .3 x + x .3 x)$

$\Rightarrow 2 (2 x^{2} + 6 x^{2} + 3 x^{2}) = 88$

$\Rightarrow 22 x^{2} = 88$

$\Rightarrow x = 2$

So sides are 2 cm, 4 cm and 6 cm

So volume $= 2 \times 4 \times 6 = 48 m^{3}$

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