Question

a cylinder has a volume of 600π cubic units. if a cone has the same base area and height as the cylinder, what is the volume of the cone? express your answer in terms of π. use the keypad to type your answer in the box provided. the volume of the cone is □ cubic units.

Explanation:

Step1: Recall the volume formulas

The volume formula for a cylinder is \(V_{cylinder}=B\times h\) (where \(B\) is the base area and \(h\) is the height). The volume formula for a cone is \(V_{cone}=\frac{1}{3}B\times h\).

Step2: Use the relationship between the volumes

Since the cone and the cylinder have the same base area (\(B\)) and height (\(h\)), and \(V_{cylinder}=600\pi = B\times h\).
Substitute \(B\times h\) into the cone's volume formula: \(V_{cone}=\frac{1}{3}(B\times h)\).
Since \(B\times h = 600\pi\), then \(V_{cone}=\frac{1}{3}\times600\pi\).

Step3: Calculate the volume of the cone

\(V_{cone}=\frac{600\pi}{3}=200\pi\)

Answer:

\(200\pi\)