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If the curved surface area of a solid right circular cylinder of height $h$ and radius $r$ is one-third of its total surface area, then

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h = \frac{1}{3} r

h = \frac{1}{2} r

h = r

h = 2 r

answer is B.

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Detailed Solution

Given that, curved surface area of a cylinder of radius "

r

" and height "h" is one-third of its total surface area.
We have to find the height of a solid right circular cylinder.
Curved surface area of a cylinder

= 2 πrh .

Total surface area of a cylinder

= 2 πr (r + h) .

According to the question,

2 πrh = \frac{1}{3} \times 2 πr (r + h)

\Rightarrow h = \frac{1}{3} \times (r + h)

\Rightarrow \frac{2}{3} h = \frac{1}{3} r

\Rightarrow h = \frac{1}{2} r

Therefore, height of a solid right circular cylinder,

h = \frac{1}{2} r

.
Hence, option 2 is correct.

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