a physical education teacher was getting ready for gym class one day . he measured the circumference of the basketball to be 9 inches when it is filled with air . he then went on to pose the following question to his classes : use 3.14

A ) how much material is needed to make four baskeballs?

b ) how much air will the four balls hold combined ?

To find the answers to these questions, we need to use the formula for the circumference of a circle:

Circumference = π * Diameter

First, let's find the diameter of the basketball. We know that the circumference is 9 inches, so we can rearrange the formula to solve for the diameter:

Diameter = Circumference / π

Diameter = 9 inches / 3.14 ≈ 2.87 inches (rounded to two decimal places)

Now that we know the diameter of the basketball, we can calculate its radius (which is half of the diameter):

Radius = Diameter / 2

Radius = 2.87 inches / 2 ≈ 1.43 inches (rounded to two decimal places)

a) To find the amount of material needed to make one basketball, we need to find the surface area of the basketball. The formula for the surface area of a sphere is:

Surface Area = 4 * π * Radius^2

Surface Area = 4 * 3.14 * (1.43 inches)^2 ≈ 25.57 square inches (rounded to two decimal places)

The amount of material needed to make one basketball is approximately 25.57 square inches.

To find the amount of material needed for four basketballs, we can multiply the surface area of one basketball by four:

Material needed for four basketballs = 4 * 25.57 square inches ≈ 102.28 square inches (rounded to two decimal places)

Therefore, approximately 102.28 square inches of material is needed to make four basketballs.

b) To find how much air the four basketballs will hold combined, we need to calculate the volume of one basketball. The formula for the volume of a sphere is:

Volume = (4/3) * π * Radius^3

Volume = (4/3) * 3.14 * (1.43 inches)^3 ≈ 9.56 cubic inches (rounded to two decimal places)

Therefore, one basketball can hold approximately 9.56 cubic inches of air.

To find how much air the four basketballs will hold combined, we can multiply the volume of one basketball by four:

Air held by four basketballs = 4 * 9.56 cubic inches ≈ 38.24 cubic inches (rounded to two decimal places)

Therefore, the four basketballs combined will hold approximately 38.24 cubic inches of air.