Question

1. if the radius of a cone is doubled, how does this affect the volume?

a. the volume is quartered.
b. the volume is halved.
c. the volume is unchanged.
d. the volume is quadrupled.

Explanation:

Step1: Recall the volume formula of a cone

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

Step2: Analyze the effect of doubling the radius

Let the original radius be \(r\), and the new radius be \(r'=2r\). The original volume \(V=\frac{1}{3}\pi r^{2}h\), and the new volume \(V'=\frac{1}{3}\pi(2r)^{2}h\). Expand \((2r)^{2}\), we get \(V'=\frac{1}{3}\pi\times4r^{2}h = 4\times(\frac{1}{3}\pi r^{2}h)\).

Answer:

d. The volume is quadrupled.