Question

A sphere of radius $r$ is inscribed in the cylinder such that the curved surface of the sphere touches the cylinder as shown in the given figure. The area of curved surface of cylinder is

• A. $\frac{4}{3}\pi r^2$
• B. $4\pi r^2$
• C. $\pi r^2$
• D. $2\pi r^2$

Answer 1

The correct option is B $4\pi r^2$

A shown in the figure, the radius of the cylinder will be $r$ and height of the cylinder will be $2r$.
$\therefore$ curved surface area of the cylinder $=$ $2\pi rh$
$=2\pi \left(r\right)\left(2r\right)$
$=4\pi r^2$