A cylinder has a diameter of 24 inches. If its height is half its radius, what is the volume of the cylinder in cubic inches?
A.
72π cu. in.
B.
864π cu. in.
C.
3,456π cu. in.
D.
6,912π cu. in.
The radius of the cylinder is half the diameter, so it is 12 inches. The height is half the radius, so it is 6 inches. The formula for the volume of a cylinder is V = πr^2h, so plugging in the values we get:
V = π(12^2)(6) = 864π
Therefore, the correct answer is B. 864π cubic inches.
To find the volume of a cylinder, we can use the formula:
Volume = π * radius^2 * height
Given that the diameter of the cylinder is 24 inches, we can find the radius by dividing the diameter by 2:
Radius = 24 inches / 2 = 12 inches
The height of the cylinder is half its radius:
Height = 1/2 * Radius = 1/2 * 12 inches = 6 inches
Substituting the values into the volume formula:
Volume = π * 12^2 * 6 = 864π cubic inches.
Therefore, the volume of the cylinder is 864π cubic inches, which corresponds to option B.