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 the cuboid is ___ $m^{3}$

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Solution

Since, the dimensions are in ratio $1 : 2 : 3$ , $\Rightarrow$ the sides = $x, 2 x, 3 x$

Total surface area $= 2 (x \times 2 x + 2 x \times 3 x + x \times 3 x)$

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

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

$\Rightarrow x^{2} = 4$

$\Rightarrow x = 2$

$∴$ , sides are $2 m, 4 m$ and $6 m$

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

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

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