Question : The curved surface area of a cylinder is five times the area of its base. Find the ratio of the radius and height of the cylinder.
Option 1: 2 : 3
Option 2: 3 : 5
Option 3: 2 : 5
Option 4: 3 : 4
Correct Answer: 2 : 5
Solution :
Given: The curved surface area of a cylinder is five times the area of its base.
Use the formulas,
The curved surface area of the cylinder = $2\pi rh$,
The area of the base of the cylinder = $\pi r^2$,
where $r$ and $h$ are the radius and height respectively.
According to the question,
$\frac{2\pi rh}{\pi r^2}=\frac{5}{1}$
⇒ $\frac{2h}{r}=\frac{5}{1}$
⇒ $\frac{r}{h}=\frac{2}{5}$
Hence, the correct answer is 2 : 5.
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