So the volume of a sphere is [tex]V= \frac{4}{3} \pi r^3[/tex] , and the volume of a cone is [tex]V= \pi r^2 \frac{h}{3} [/tex] (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.)
[tex]V= \frac{4}{3} \pi 3^3[/tex]
Solve the exponents to get [tex]V= \frac{4}{3} \pi 9[/tex]
Multiply 4/3 and 9 to get [tex]V=13.5 \pi [/tex]
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.
[tex]13.5 \pi = \pi 3^2 \frac{h}{3}[/tex]
Solve the exponents to get [tex]13.5 \pi =9 \pi \frac{h}{3} [/tex]
Divide [tex]9 \pi [/tex] on each side to get [tex]1.5= \frac{h}{3} [/tex]
Multiply 3 on each side, and your answer should be [tex]4.5=h[/tex]
