Question

suppose the radius of a sphere is tripled.
a. what happens to its surface area?
b. what happens to its volume?

Answer 1

$A=4r^2\pi \\r_1=4r \\A_1=4r_1^2\pi=4(4r)^2\pi=4\times16r^2\pi=16\times4r^2\pi=16A$
The surface area is increased 16 times.

$V= \frac{4}{3} r^3\pi \\ \\r_1=4r \\ \\V_1=\frac{4}{3} r_1^3\pi=\frac{4}{3} (4r)^3\pi=\frac{4}{3} \times64r^3\pi=64\times\frac{4}{3} r^3\pi=64V$
The volume is increased 64 times.