Question

If $S_1$ and $S_2$ be the surface area of a sphere and the curved surface of the circumscribed cylinder then $S_1$ is equal to

• A. $S_2$
• B. $2S_2$
• C. $\frac{1}{2}{S}_2$
• D. $\frac{2}{3}{S}_2$

Answer 1

The correct option is A $S_2$

Let the radius of the sphere be $r.$ Then the radius of the circumscribing cylinder will be $r$ as well.

Height$\left(H\right)$ of the cylinder will be equal to the diameter of the sphere that is equal to $2r$.

So, the surface area of the sphere will be $S_1=4\pi r^2\dots \left(i\right)$

And, curved surface area of the cylinder,

$S_2=2\pi rH$

$=\left(2\pi r\right)2r$

$=4\pi r^2\dots \left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$, we can conclude that $S_1=S_2$.

Hence, option $A$ is correct.