Question

A sphere has a radius of $7\text{cm}$. If the radius is increased to $14\text{cm}$, calculate the change in the surface area of the sphere.

• A. $788\pi {\text{cm}}^2$
• B. $588\pi {\text{cm}}^2$
• C. $888\pi {\text{cm}}^2$
• D. $688\pi {\text{cm}}^2$

Answer 1

The correct option is B $588\pi {\text{cm}}^2$

We know that,
the surface area of sphere
$=4\pi {\text{r}}^2$

Given that,
initial radius of sphere $=7\text{cm}$
final radius of sphere $=14\text{cm}$

Now,
change in surface area of sphere
= final surface area of sphere - initial surface area of sphere
= $4\pi \times {14}^2$ - $4\pi \times 7^2$
=$4\pi \times ({14}^2-7^2)$
=$4\pi \times \left(147\right)$
= $588\pi {\text{cm}}^2$