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. 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.

Answer 1

Answer:

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

Step-by-step explanation:

step 1

Find the height of the cone

The volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

substitute the given values

$V=9\pi\ in^3\\r=6/2=3\ in$

$9\pi=\frac{1}{3}\pi 3^{2} h$

simplify

$9\pi=3\pi h\\h=3\ in$

step 2

Find the volume of the cylinder

The volume is equal to

$V=\pi r^{2} h$

substitute the given values

$h=3\ in\\r=3\ in$

$V=\pi 3^{2} (3)\\V=27\pi\ in^3$

step 3

Compare the volumes

The volumes are not equal

Answer 2

Answer:

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

Step-by-step explanation:

Got it right on the test.