What is the surface area of a sphere when given the volume?

Answer 1

The volume of a sphere is given by the formula 4/3 *pi*r^3 and the surface area is given by the formula 4*pi*r^2. If you know the volume of the sphere you can solve for the radius, then you can plug the resulting value into the surface area formula. For example, suppose I knew that the volume of a sphere was 25 cubic meters:

Set 25 equal to the voume formula:

4/3*pi*r^3 = 25

multiply both sides by 3/4 and divide both sides by pi:

r^3=pi*75/4

take the cube root of both sides:

r=(pi*75/4)^(1/3)

Now plug r into my formula for surface area:

4*pi*r^2 = 4*pi*((pi*75/4)^(1/3))^2

And I probably want a decimal approximation for the surface area, that is, I probably want to get rid of the pis and the fractional exponent, so I can plug 4*pi*((pi*75/4)^(1/3))^2 into a calculator to get 190.24385. Then a sphere with a volume of 25 cubic meters has a surface area of 190.24385 square meters.