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.

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

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

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

$\frac{{SA}_2}{{SA}_1}$ = $\frac{4\pi {r_2}^2}{4\pi {r_1}^2}$

= $\frac{4\pi \left(4r_1{)}^2\right)}{4\pi {r_1}^2}$ = 16.