Question

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is:

• A. 2 : 1
• B. 1 : 2
• C. 2 : 3
• D. 3 : 2

Hint:

For minimum surface area with fixed volume, height should be twice the radius in a closed cylinder.

Answer 1

The Correct Option is A

Let radius = \( r \), height = \( h \), volume \( V = \pi r^2 h \) is constant.
Surface area \( S = 2\pi r^2 + 2\pi rh \).
Using \( h = \frac{V}{\pi r^2} \) and substituting into surface area, minimize \( S \) using calculus.
After optimization, we get \( h = 2r \), so the ratio \( h : r = 2 : 1 \).