Question:
Mark (✓) against the correct answer:
The length, breadth and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm3. The whole surface area of the cuboid is
(a) 216 cm2
(b) 324 cm2
(c) 432 cm2
(d) 460 cm2
Solution:
(c) $432 \mathrm{sq} \mathrm{cm}$
Volume $=l b h=3 x \times 4 x \times 6 x=72 x^{3}=576 \mathrm{~cm}^{3}$
$\Rightarrow x=\sqrt[3]{\frac{576}{72}}=2$
$\therefore$ Total surface area $=2(l b+b h+l h)=2(3 x 4 x+4 x 6 x+3 x 6 x)=2(48+96+72)=432 \mathrm{~cm}^{2}$
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