Question

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: Write the formula for the volume 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 new volume when height is doubled

Let the original height be \(h_1 = h\) and the new height be \(h_2=2h\), with radius \(r_1 = r_2=r\).
The original volume \(V_1=\frac{1}{3}\pi r^{2}h\).
The new volume \(V_2=\frac{1}{3}\pi r^{2}(2h)\).

Step3: Simplify the new - volume expression

\(V_2 = 2\times(\frac{1}{3}\pi r^{2}h)\).
Since \(V_1=\frac{1}{3}\pi r^{2}h\), we have \(V_2 = 2V_1\).

So when the height of a cone is doubled and the radius remains the same, the new volume is doubled.

Answer:

D. Doubled