Jessica's company makes solid metal balls for various industrial uses. A customer wants aluminum balls that have a diameter of 6in. If Jessica must make 70 of these balls, how much aluminum will she need?
Question
Jessica's company makes solid metal balls for various industrial uses. A customer wants aluminum balls that have a diameter of 6in. If Jessica must make 70 of these balls, how much aluminum will she need?
Solution
To solve this problem, we first need to find the volume of one ball. The formula for the volume of a sphere is V = 4/3 * π * r^3, where r is the radius of the sphere.
Step 1: Find the radius. The diameter of the ball is 6 inches, so the radius is half of that, which is 3 inches.
Step 2: Substitute the radius into the volume formula: V = 4/3 * π * (3in)^3 = 36π cubic inches.
Step 3: Multiply the volume of one ball by the number of balls to find the total volume of aluminum needed. 36π cubic inches/ball * 70 balls = 2520π cubic inches.
So, Jessica will need 2520π cubic inches of aluminum to make 70 balls.
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