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*16r^2\pi=16*4r^2\pi=16A`
The surface area is increased 16 times.


`V= (4)/(3) r^3\pi \\ \\r_1=4r \\ \\V_1=(4)/(3) r_1^3\pi=(4)/(3) (4r)^3\pi=(4)/(3) *64r^3\pi=64*(4)/(3) r^3\pi=64V`
The volume is increased 64 times.