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

48 m^{3}

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96 m^{3}

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24 m^{3}

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32 m^{3}

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Solution

The correct option is A $48 m^{3}$
Given the ratio of the dimensions = 1:2:3.
Let the sides be $x, 2 x, 3 x$ .

Total surface area of a cuboid = 2(lb+bh+hl)
$= 2 (x .2 x + 2 x .3 x + x .3 x)$

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

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

$\Rightarrow x^{2} = 4 m o r x = 2 m$

Hence, the sides are 2m, 4m and 6m

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

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Similar questions

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.

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 ___ $m^{3}$

88 m^{2}

1 : 2 : 3

88 m^{2}

1 : 2 : 3

88 m^{2}

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