Question

The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume oft
prism?
h
base area = B
base area =B

Answer 1

Answer:

$ratio=\frac{1}{3}$

Step-by-step explanation:

step 1

Find the volume of the cone

The volume of the cone is equal to

$V_c=\frac{1}{3}Bh$

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

$V_p=Bh$

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

$ratio=\frac{V_c}{V_p}$

substitute the values

$ratio=\frac{\frac{1}{3}Bh}{Bh}$

simplify

$ratio=\frac{1}{3}$