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The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm². The volume of the cuboid is
(a) 48 cm³
(b) 64 cm³
(c) 96 cm³
(d) 120 cm³

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Solution

(a) $48 c m^{3}$

Let a be the length of the smallest edge.
Then the edges are in the proportion a : 2a : 3a.
Now, surface area $= 2 (a \times 2 a + a \times 3 a + 2 a \times 3 a) = 2 (2 a^{2} + 3 a^{2} + 6 a^{2}) = 22 a^{2} = 88 c m^{2}$
$\Rightarrow a = \sqrt{\frac{88}{22}} = \sqrt{4} = 2$
Also, 2a = 4 and 3a = 6
∴ Volume $= a \times 2 a \times 3 a = 2 \times 4 \times 6 = 48 c m^{3}$

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