Question

A cube and a cylinder have identical heights and an identical base radius. Nevaeh knows the volume of the cylinder. What must she do to find the volume of the cone?

Answer 1

To find the volume of the cone after knowing the volume of the cylinder, Nevaeh needs to follow these steps:

1. **Understand the Volume of the Cylinder**: The formula for the volume of a cylinder is given by:
\[
V_{\text{cylinder}} = \pi r^2 h
\]
where \( r \) is the radius of the base and \( h \) is the height.

2. **Find the Dimensions**: Since the cone has the same height \( h \) and base radius \( r \) as the cylinder, Nevaeh can use the radius and height values of the cylinder for the cone.

3. **Use the Cone Volume Formula**: The formula for the volume of a cone is given by:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]

4. **Calculate the Volume of the Cone**: Since Nevaeh knows the volume of the cylinder, she can find the volume of the cone by taking one-third of the volume of the cylinder. Specifically:
\[
V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}}
\]

In summary, Nevaeh must take the volume of the cylinder and divide it by 3 to find the volume of the cone.