Question

Find the volume in terms of pi of a sphere with a surface area of 9 pi square feet

Answer 1

Explanation:

Answer 2

So we want to know the volume of a sphere in terms of pi if we know the area of the sphere is equal to A=9pi. So the area of the sphere is A=4*pi*r^2 and the volume V=(4/3)*pi*r^3. We can get the radius from the area: 9pi=4*pi*r^2 and we see the pi cancels out: 9=4*r^2. We divide by 4 and take the square root: r=sqrt(9/4)=3/2. So r=3/2 and we can input it into volume V.

V=(4/3)*(3/2)^3*pi=(4/3)*(27/8)*pi=(9/4)*pi.

So the volume of the sphere is V=(9/4)*pi cubic feet.