Answer:
9 cm
Step-by-step explanation:
Use the cone volume formula, V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
Plug in the volume and radius, and solve for h, the height:
V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
27[tex]\pi[/tex] = [tex]\pi[/tex](3²)[tex]\frac{h}{3}[/tex]
27[tex]\pi \\[/tex] = 9[tex]\pi[/tex][tex]\frac{h}{3}[/tex]
3 = [tex]\frac{h}{3}[/tex]
9 = h
So, the height of the cone is 9 cm
