The dimensions of a cuboid are in the ratio of 1:2:3 and its total surface area is 352 $m^{2}$ . Find its volume.

384 m^{3}

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348 m^{3}

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438 m^{3}

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None of the above

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Solution

The correct option is A $384 m^{3}$
The sides will be $x, 2 x, 3 x$

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

$\Rightarrow 2 (2 x^{2} + 6 x^{2} + 3 x^{2}) = 352$
$\Rightarrow 22 x^{2} = 352$
$\Rightarrow x^{2} = 16$
$\Rightarrow x = 4$

So sides are 4 m, 8 m and 12 m

So volume $= 4 m \times 8 m \times 12 m = 384 m^{3}$

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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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88 m^{2}

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