Question

If the height of the cylinder is doubled, by what number must the radius of the base be multiplied so that resulting cylinder has the same curved surface area as the original cylinder?

• A. 2
• B. 4
• C. 0.5
• D. 0.25

Answer 1

The correct option is C 0.5

Let the initial radius of the cylinder is R and the final radius of the cylinder is r.
H is the height of the cylinder.

Initial curved surface area of cylinder = 2 πRH

Final curved surface area of cylinder = 2π r(2H)

According to the question, initial and final curved surface areas remains equal.

Thus, 2π RH = 2π r(2H)
$\Rightarrow \text{r}=\frac{1}{2}\text{R}$