Question

1. if the radius of a cylinder is doubled, the volume will increase by a factor of

a. 8
b. 4
c. 2
d. 3

Explanation:

Step1: Write the formula for the volume of a cylinder

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

Step2: Find the new volume when the radius is doubled

If the radius is doubled (\(r_{new}=2r\)), the new volume \(V_{new}=\pi(2r)^{2}h\). Expand \((2r)^{2}\): \(V_{new}=\pi\times4r^{2}h = 4(\pi r^{2}h)\).
Since \(V=\pi r^{2}h\), then \(V_{new} = 4V\).

Answer:

B. 4