Question

A cylinder has an 18-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed within the cylinder, and then the cylinder is filled with water. How much water is in the cylinder? Give your answer in terms of pi.

A. 1.162π in
B. 1.179π in
C. 1.215π in
D. 1.251π in

Answer 1

The amount of water in the cylinder is 1179π cubic inches.

Step-by-step explanation:

To find the amount of water in the cylinder, we need to calculate the volume of the cylinder and then subtract the volume of the ball. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. In this case, the radius is half the diameter, so it is 9 inches. Plugging in the values, we get V = π(9 inches)²(15 inches) = 1215π cubic inches.

Next, we need to find the volume of the ball. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. In this case, the radius is half the diameter, so it is 3 inches. Plugging in the values, we get V = (4/3)π(3 inches)³ = 36π cubic inches.