Question

If the radius of a sphere is increased by $2$cm, then its surface area increases by $352c{m}^2$. The radius of the sphere before the increase was _________.

• A. $3$cm
• B. $4$cm
• C. $5$cm
• D. $6$cm

Answer 1

The correct option is D $6$cm

Let the radius of the sphere before increase$=r$.

Given, increased surface area $=352c{m}^2$.

Also, the surface area of the sphere before the increase is $A=4\pi r^2$.

After increasing radius by $2cm$, the area is increased by $352c{m}^2$.

Applying the above conditions:

$\therefore 4\pi r^2+352=4\pi (r+2{)}^2$

$\Rightarrow 352=16\pi +16\pi r$

$\Rightarrow 1+r=\frac{352}{16\pi }=7$

$\Rightarrow r=6cm$.

Hence, option $D$ is correct.