The volume of a cylinder is 32.25 cubic inches. If a cone has the same height and radius as the cylinder, what is its volume?

Respuesta :

gmany

The volume of a cylinder with a radius r and a height h:

[tex]V_1=\pi r^2h[/tex]

The volume of a cone with a radius r and a height h:

[tex]V_2=\dfrac{1}{3}\pi r^2h[/tex]

Therefore

[tex]V_2=\dfrac{1}{3}V_1[/tex]

We have [tex]V_1=32.25\ in^3[/tex]

Substitute:

[tex]V_2=\dfrac{1}{3}\cdot32.25=10.75\ in^3[/tex]

Answer: The volume of a cone is equal 10.75 in³