Question

1. if the height of a cone is doubled and the radius remains the same, the new volume will be:

a. tripled
b. halved
c. unchanged
d. 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: Calculate the new volume

Let the original height be \(h\) and the new height be \(h_{new} = 2h\), with radius \(r\) remaining the same. The new volume \(V_{new}=\frac{1}{3}\pi r^{2}h_{new}\). Substitute \(h_{new} = 2h\) into the formula, we get \(V_{new}=\frac{1}{3}\pi r^{2}(2h)=2\times(\frac{1}{3}\pi r^{2}h)\). Since \(V = \frac{1}{3}\pi r^{2}h\), then \(V_{new}=2V\).

Answer:

d. Doubled