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?

1 answer

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.