Question

a cone has a volume of 144π in³ and a diameter of 12 in. wilson states that a cylinder with the same height and diameter has the same volume. which statement explains whether or not wilson is correct? a cylinder in which h = 12 and d = 12 has a volume of 144π in³; therefore, wilson is correct a cylinder in which h = 4 and d = 12 has a volume of 144π in³; therefore, wilson is correct a cylinder in which h = 12 and d = 12 has a volume of 432π in³; therefore, wilson is incorrect a cylinder in which h = 4 and d = 12 has a volume of 432π in³; therefore, wilson is incorrect

Explanation:

Step1: Calculate the radius

Given diameter \(d = 12\), radius \(r=\frac{d}{2}=6\)

Step2: Recall the volume formula for a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\)

Step3: Substitute \(h = 12\) and \(r = 6\) into the formula

\(V=\pi\times6^{2}\times12=\pi\times36\times12 = 432\pi\)

Answer:

A cylinder in which \(h = 12\) and \(d = 12\) has a volume of \(432\pi\) in³; therefore, Wilson is incorrect.