Question : The sum of the length and breadth of a cuboid is 40 cm. If the height of the cuboid is $\frac{1}{5}$ of the sum of its length and breadth, then what is the lateral surface area of the cuboid?
Option 1: $580 {~cm}^2$
Option 2: $320 {~cm}^2$
Option 3: $640 {~cm}^2$
Option 4: $720 {~cm}^2$
Correct Answer: $640 {~cm}^2$
Solution :
The sum of the length ($l$) and breadth ($b$) is 40 cm
⇒ $l+ b = 40$ cm
The height of the cuboid = $\frac{1}{5}(l+b)$
= $\frac{1}{5}(40)$ = 8 cm
lateral surface area (L.S.A) of the cuboid = 2$(l+b)$ × height, where
$l$ = length; $b$ = breadth
⇒ L.S.A = 2 × 40 × 8
= 640 cm
2
Hence, the correct answer is $640 ~cm^2$.
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