Question : The length, breadth, and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm3. The whole surface of the cuboid is:
Option 1: 216 cm2
Option 2: 324 cm2
Option 3: 432 cm2
Option 4: 460 cm2
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Correct Answer: 432 cm 2
Solution :
Volume of cuboid = 576 cm
2
The ratio of length, breadth, and height of a cuboid = 3 : 4 : 6
Let the length, $l$ = $3x$, breadth, $b$ = $4x$, and height, $h$ = $6x$.
Volume of cuboid = $l×b×h$ = $3x×4x×6x$
⇒ 576 = 72$x^{3}$
⇒ $x^{3}$ = 8
⇒ $x$ = 2
So, $l$ = $3x$ = 6 cm
$b$ = $4x$ = 8 cm
$h$ = $6x$ = 12 cm
Total surface area = $2(lb+bh+hl)$
= 2 × (6 × 8 + 8 × 12 + 12 × 6)
= 2 × (48 + 96 + 72)
= 432 cm
2
Hence, the correct answer is 432 cm
2
.
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