Answer:
The height of the cone is [tex]17\ in[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
In this problem we have
[tex]r=12/2=6\ in[/tex] ----> the radius is half the diameter
[tex]V=640.88\ in^{3}[/tex]
assume [tex]\pi=3.14[/tex]
substitute the values and solve for h
[tex]640.88=\frac{1}{3}(3.14)(6)^{2}h[/tex]
[tex]h=640.88*3/((3.14)(36))=17\ in[/tex]
