Question

1. what happens to the volume of a cone if the height is tripled while the radius remains constant?

the volume is tripled
the volume is halved
the volume remains unchanged
the volume is doubled

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is \(V = \frac{1}{3}\pi r^{2}h\), where \(r\) is the radius 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 \(V_1=\frac{1}{3}\pi r^{2}h_1\), and the new volume \(V_2=\frac{1}{3}\pi r^{2}h_2\). Substitute \(h_2 = 3h_1\) into the formula for \(V_2\), we get \(V_2=\frac{1}{3}\pi r^{2}(3h_1)=3\times(\frac{1}{3}\pi r^{2}h_1)\). Since \(V_1 = \frac{1}{3}\pi r^{2}h_1\), then \(V_2 = 3V_1\).

Answer:

The volume is tripled.