Question

if the radius of a cylinder is doubled while keeping the height the same, how does its volume change? a. it quadruples b. it triples c. it stays the same d. it doubles

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 the radius is doubled

Let the original radius be \(r\), and the new radius \(r_{new}=2r\), height \(h_{new} = h\). The new volume \(V_{new}=\pi(2r)^{2}h\).

Step3: Simplify the new - volume formula

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Since \(V=\pi r^{2}h\), then \(V_{new} = 4V\). So the volume quadruples.

Answer:

A. It quadruples