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?

Options :

A. A cylinder in which h = 1 and d = 6 has a volume of 27π in3; therefore, Wilson is correct.

B. A cylinder in which h = 3 and d = 6 has a volume of 27π in3; therefore, Wilson is incorrect.

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

D. A cylinder in which h = 3 and d = 6 has a volume of 9π in3; therefore, Wilson is correct.

B. A cylinder in which h = 3 and d = 6 has a volume of 27π in3; therefore, Wilson is incorrect

Step-by-step explanation:

Given the following :

The volume of cone = 9π in^3

Diameter= 6 in

Wilson's statement: Wilson states that a cylinder with the same height and diameter has the same volume

Firstly:

Let's calculate the height of the cone

The volume(V) of a cone = (1/3)πr^2h

h = height, r = radius = diameter/2 = 6/2 = 3 in

V = (1/3) * π * 3^2 * h

9π = 1/3 * π * 9 * h

9π = 9πh / 3

3 * 9π = 9πh

Divide both sides by 9π

h = 3

Now calculating the volume of a cylinder:

Volume(V) of a cylinder = πr^2h

V = π * 3^2 * 3

V = π * 9 * 3

V = 27π in^3

Both volumes are different, therefore Wilson is incorrect