The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface a

Question

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}

Answer:
:
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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