Answer:
The height of the cone is [tex]4\ in[/tex]
Step-by-step explanation:
step 1
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi (r)^{2}(h)[/tex]
substitute the values
[tex]V=\pi (2)^{2}(3)=12\pi\ in^{3}[/tex]
step 2
Find the height of the cone
The volume of the cone is equal to
[tex]V=(1/3)\pi (r)^{2}(h)[/tex]
Remember that the volume of the cone is equal to the volume of the cylinder
substitute the given values and solve for h
[tex]12\pi=(1/3)\pi (3)^{2}(h)[/tex]
Simplify
[tex]36=9(h)[/tex]
[tex]h=36/9=4\ in[/tex]
