Question

1. if the height of a cylinder is tripled, the volume will ____.

a. double
b. halve
c. remain the same
d. triple

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 of the base and \(h\) is the height.

Step2: Analyze the effect of tripling the height

Let the original height be \(h_{1}\) and the new height be \(h_{2}=3h_{1}\). The original volume \(V_{1}=\pi r^{2}h_{1}\), and the new volume \(V_{2}=\pi r^{2}h_{2}\). Substitute \(h_{2} = 3h_{1}\) into the formula for \(V_{2}\), we get \(V_{2}=\pi r^{2}(3h_{1}) = 3(\pi r^{2}h_{1})\). Since \(V_{1}=\pi r^{2}h_{1}\), then \(V_{2} = 3V_{1}\).

So when the height of a cylinder is tripled, the volume will triple.

Answer:

D. triple