Question

question 4 of 10
a cone has one - third times the volume of a cylinder with the same base and altitude.
a. true
b. false

Explanation:

Step1: Volume formula of cylinder

The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height (altitude).

Step2: Volume formula of cone

The volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height (altitude).

Step3: Compare the two volumes

If a cone and a cylinder have the same base (so the same \(r\)) and the same altitude (\(h\)), then by comparing \(V_{cone}=\frac{1}{3}\pi r^{2}h\) and \(V_{cylinder}=\pi r^{2}h\), we can see that \(V_{cone}=\frac{1}{3}V_{cylinder}\).

Answer:

A. True