Question : The height and curved surface area of a right circular cylinder are $7~\text{cm}$ and $70\pi~\text{cm}^2$. Its total surface area is:
Option 1: $140 \pi~\text{cm}^2$
Option 2: $150 \pi~\text{cm}^2$
Option 3: $180 \pi~\text{cm}^2$
Option 4: $120 \pi~\text{cm}^2$
Correct Answer: $120 \pi~\text{cm}^2$
Solution :
The curved surface area of a right circular cylinder, where $r$ is the radius and $h$ is the height $= 2\pi r h$
Given that the curved surface area is $70\pi~\text{cm}^2$ and the height is $7~\text{cm}$,
$⇒70\pi = 2\pi r \times 7$
$⇒r = \frac{70}{2 \times 7} = 5~\text{cm}$
The total surface area of a cylinder,
$= 2\pi r(h + r)$
$= 2\pi \times 5(7 + 5) = 10\pi \times 12 = 120\pi~\text{cm}^2$
Hence, the correct answer is $120\pi~\text{cm}^2$.
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