Question

Karen's company makes solid metal balls for various industrial uses. A customer wants copper balls that have a diameter of 3 in. If Karen must make 90 of these balls, how much copper will she need?

Use 3.14 for n, and do not round your answer.

Answer 1

The volume of a sphere is given by the formula V = 4/3 * pi * r^3, where r is the radius of the sphere. Since the diameter of the copper balls is given as 3 inches, the radius is 1.5 inches. Plugging this into the formula, we get V = 4/3 * 3.14 * (1.5)^3 = 14.13 cubic inches per ball.

To find the total volume of copper needed to make 90 balls, we can multiply the volume of one ball by the number of balls: 14.13 cubic inches/ball * 90 balls = 1,271.7 cubic inches of copper.

Answer 2

The volume of a sphere is given by the formula V = (4/3) * pi * r^3, where r is the radius of the sphere.

Since the diameter of the copper balls is 3 inches, the radius is 1.5 inches (half of the diameter).

The volume of one copper ball is therefore:

V = (4/3) * 3.14 * (1.5)^3
V = 14.13 cubic inches

To make 90 copper balls, Karen will need:

90 * 14.13 = 1271.7 cubic inches of copper

Therefore, Karen will need 1271.7 cubic inches of copper to make 90 copper balls with a diameter of 3 inches.