The volume of a sphere is 5,000pi m3. What is the surface area of the sphere to the nearest square meter?

Question

kinggeorge · Answer

The volume of a sphere is given by $$V={4 \over 3}\pi r^3$$and the surface area is given by $$A=4 \pi r^2$$Since we have volume, we can backtrack to find the radius, and then the surface area. So, $$5000\pi={4 \over 3}\pi r^3$$$$3750=r^3$$$$r=\sqrt[3]{3750}$$Now, we can substitute in to find the surface area.$$A=4\pi (\sqrt[3]{3750})^2$$We can evaluate this with a calculator to get 

3033 m^2

kinggeorge · Answer

To be more precise, we get $$V\approx 3033.1743577959768605787928419 \;\;\;m^2$$which rounds to $$V\approx3033\;\;\;m^2$$