Asphere and the base of a cone have a radius of 3 inches. the volume of the sphere equals the volume of the cone. what is the height of the cone, in inches?

So the volume of a sphere is  , and the volume of a cone is  (h=height, r=radius). Knowing only the radius, we can solve for the volume of the sphere. (Also I'm going to be leaving answers in pi form.)


Solve the exponents to get 
Multiply 4/3 and 9 to get 

Now that we know the volume of the sphere, we can solve for the height of the cone since the volumes for both are the same.



Solve the exponents to get 

Divide  on each side to get 

Multiply 3 on each side, and your answer should be