Question

Find the change in surface area of a sphere if its radius is increased 4 times.

• A. Surface area increases 2 times
• B. Surface area increases 16 times
• C. Surface area decreases 2 times
• D. Surface area decreases 16 times

Answer 1

The correct option is B

Surface area increases 16 times

Surface area of a sphere is given as
4$\pi$$r^2$, where r is the radius of the sphere.

Let the initial radius be $r_1$ and the final radius be $r_2$.

${SA}_1$ = 4$\pi$${r_1}^2$

${SA}_2$ = 4$\pi$${r_2}^2$

Also, $r_2$ = ${4r}_1$

Now,
$\frac{{SA}_2}{{SA}_1}=\frac{4\pi {r_2}^2}{4\pi {r_1}^2}=\frac{4\pi (4r_1{)}^2}{4\pi {r_1}^2}=\frac{4\pi \left(16r_1^2\right)}{4\pi {r_1}^2}=16$

$\therefore$ Surface area of a sphere increases by 16 times when its radius is increased four times.