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.B cylinder in which h = 4 and d = 12 has a volume of 144π in3; therefore, Wilson is correct.C cylinder in which h = 12 and d = 12 has a volume of 432π in3; therefore, Wilson is incorrect.D cylinder in which h = 4 and d = 12 has a volume of 432π in3; therefore, Wilson is incorrect.

Answer 1

Okay, here we have this:

Considering the provided information and measures, we are going to calculate the requested height and volume of the cylinder, so we obtain the following:

First finding the volume of the cone we have:

Volume of a cone:

V = (1/3)πr^2h

144π in^3 = (1/3)π(12in/2)^2h

144π in^3 = (1/3)π(6in)^2h

144π in^3 = (1/3)π*36in^2h

144π in^3 = 12π in^2*h

h=144π in^3 /12π in^2

h=12 in

Now, let's find the volume of the cylinder with radius equal to 6in and height equal to 12in:

V = πr^2*h

V = π(6 in)^2*(12 in)

V = π(36 in^2)*(12 in)

V = 432π in^3

Finally we obtain that a cylinder in which h = 12 and d = 12 has a volume of 432π in3; therefore, Wilson is incorrect. Then the correct answer is the option C.