Question

An inflatable ball can be modeled as a hollow sphere. Miguel

measures the outer diameter of the ball to be 50 cm. If the
material that makes up the ball has a thickness of 1.25 cm, find
the total volume of material that makes up the ball. Round your
answer to the nearest hundredth if necessary. (Note: diagram is
not drawn to scale.)

Answer 1

The total volume of material that makes up the ball is 5,394.24 cm³.

Step-by-step explanation:

To find the total volume of material that makes up the ball, we need to calculate the volume of the sphere formed by the outer diameter and subtract the volume of the sphere formed by the inner diameter.

To calculate the volume of a sphere, we use the formula V = (4/3)πr³, where r is the radius.

The outer diameter of the ball is 50 cm, so the radius is 25 cm. The volume of the outer sphere is (4/3)π(25 cm)³ = 65,449.85 cm³.

The inner diameter of the ball is 50 cm - 2(1.25 cm) = 47.5 cm, so the radius is 23.75 cm. The volume of the inner sphere is (4/3)π(23.75 cm)³ = 60,055.61 cm³.

Finally, we can subtract the volume of the inner sphere from the volume of the outer sphere to find the total volume of material that makes up the ball: 65,449.85 cm³ - 60,055.61 cm³ = 5,394.24 cm³.