Answer:
[tex]ratio=\frac{1}{3}[/tex]
Step-by-step explanation:
step 1
Find the volume of the cone
The volume of the cone is equal to
[tex]V_c=\frac{1}{3}Bh[/tex]
where
B is the area of the circular base
h is the height of the cone
step 2
Find the volume of the prism
The volume of the cone is equal to
[tex]V_p=Bh[/tex]
where
B is the area of the base of the prism
h is the height of the prism
step 3
Find the ratio of the volume of the cone to the volume oft the prism
[tex]ratio=\frac{V_c}{V_p}[/tex]
substitute the values
[tex]ratio=\frac{\frac{1}{3}Bh}{Bh}[/tex]
simplify
[tex]ratio=\frac{1}{3}[/tex]
