Can you explain how to do this?

Question

You've been asked to help decorate for a school dance, and the theme chosen is "The Solar System." The plan is to have a bunch of papier-mâché spheres serve as models of the planets, and our job is to paint them. How can you write a simplified equation using rational exponents for the surface area of a sphere in terms of its volume? 

(The formula for the volume of a sphere is V=4/3πr^3 and the formula for the surface area of a sphere is A=4πr^2.) 

Answer 1

A_sp=3V_sp/r = the surface area of the sphere.

 

Where V_sp=volume of sphere=4/3*π*r^3.

 

3V_sp/r=3(4/3*π*r^3)/r=4π*r^2=A_sp

 

Answer 2

A = 4πr²

A/4 = πr²

 

V = (4/3)πr³

3V/4 = πr³

3V/4r = π²

                            Set the two equal to each other.

A/4 = 3V/4r

A = 3V/r