Question : The sum of the radius of the base and the height of a cylinder is 42 m. If the total surface area of the cylinder is 6336 m2, find the curved surface area of the cylinder correct to two places of decimals (use $\pi=\frac{22}{7}$).
Option 1: 2157.43 m2
Option 2: 2571.43 m2
Option 3: 2715.43 m2
Option 4: 2517.43 m2
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Correct Answer: 2715.43 m 2
Solution :
Let the radius and height of the cylinder be $r$ and $h$ m.
Given, $r+h=42$ m
The total surface area of the cylinder = 6336 m
2
$⇒2\pi r(r+h)=6336$
$⇒2\times \frac{22}{7}\times r\times 42 = 6336$
$⇒r = 24$ m
So, $h=42-24=18$ m
Curved surface area of cylinder = $2\pi rh=2\times \frac{22}{7}\times 24\times 18= 2715.43$ m
2
Hence, the correct answer is 2715.43 m
2
.
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