Question

the volume of a cone is 36π cubic units. What is the volume of a cylinder that has the same base area and the same height?

Answer 1

The volume of a cylinder with the same base and height as a given cone is three times the volume of the cone, so if the cone's volume is 36π cubic units, the cylinder's volume would be 108π cubic units.

Step-by-step explanation:

The question involves finding the volume of a cylinder when the volume of a cone with identical base and height is given. Since the volume of a cone is one-third the volume of a cylinder with the same base area and height, we can find the volume of the cylinder by using the formula for the volume of a cylinder, V = πr²h, and multiplying the given cone's volume by 3. Therefore, if the volume of the cone is 36π cubic units, the volume of the cylinder would be 108π cubic units, because the volume of the cone is exactly one-third of the volume of a cylinder.

Answer 2

V_cone = 1/3 pi * r^2 * h
V_cylinder = pi*r^2*h

If you multiply the cone's volume by 3 then you get the cylinder's volume. They become the same formula
3 V_cone = pi r^2 h
Since the cone's volume is 36pi They cylinder's volume is 3*36pi = 108 pi