Question:
Tick (✓) the correct answer:
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
Solution:
(a) $48 \mathrm{~cm}^{3}$
Let $a$ be the length of the smallest edge.
Then the edges are in the proportion $a: 2 a: 3 a$.
Now, surface area $=2(a \times 2 a+a \times 3 a+2 a \times 3 a)=2\left(2 a^{2}+3 a^{2}+6 a^{2}\right)=22 a^{2}=88 \mathrm{~cm}^{2}$
$\Rightarrow a=\sqrt{\frac{88}{22}}=\sqrt{4}=2$
Also, $2 a=4$ and $3 a=6$
$\therefore$ Volume $=a \times 2 a \times 3 a=2 \times 4 \times 6=48 \mathrm{~cm}^{3}$