Question

a cone has a volume of 9π in³ and a diameter of 6 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 = 3 and d = 6 has a volume of 9π in³, therefore, wilson is correct. a cylinder in which h = 1 and d = 6 has a volume of 9π in³, therefore, wilson is correct. a cylinder in which h = 3 and d = 6 has a volume of 27π in³, therefore, wilson is incorrect. a cylinder in which h = 1 and d = 6 has a volume of 27π in³, therefore, wilson is incorrect.

Explanation:

Step1: Recall volume formula for cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height. Given $d = 6$, then $r=\frac{d}{2}=3$.

Step2: Calculate volume for different height - radius cases

Case 1: If $h = 1$ and $r = 3$, then $V=\pi\times3^{2}\times1=9\pi$.
Case 2: If $h = 3$ and $r = 3$, then $V=\pi\times3^{2}\times3 = 27\pi$.

Wilson says a cylinder with the same height and diameter as the cone has the same volume. The volume of the cone is $9\pi$ and the diameter $d = 6$ (so $r = 3$). For a cylinder with $h = 1$ and $r=3$, $V = 9\pi$.

Answer:

A cylinder in which h = 1 and d = 6 has a volume of 9π in³, therefore, Wilson is correct.