Question

1. what happens to the volume of a cylinder if both the radius and height are doubl

a. the volume increases by a factor of 8.
b. the volume stays the same.
c. the volume triples.
d. the volume increases by a factor of 6

Explanation:

Step1: Recall the volume formula 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: Calculate the new volume when \(r\) and \(h\) are doubled

If the radius becomes \(2r\) and the height becomes \(2h\), the new volume \(V_{new}=\pi(2r)^{2}(2h)\).
Simplify \(V_{new}\):

$$
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Since the original volume \(V=\pi r^{2}h\), we can see that \(V_{new} = 8V\).

Answer:

A. The volume increases by a factor of 8.