Question

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

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

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

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

$$
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Since \(V = \pi r^{2}h\), we can see that \(V'=8V\).

Answer:

D. The volume increases by a factor of 8.