Use the formula for the volume of a sphere to solve the following problem. How much air is needed to fill a basketball with a diameter of 9 inches? Use 3.14 as an approximation for pi. Round your answer to the nearest tenth.
The formula for the volume of a sphere is given by V = (4/3)πr^3, where r is the radius of the sphere.
In this problem, the basketball has a diameter of 9 inches, so the radius is equal to half the diameter, which is 9/2 = 4.5 inches.
Substituting this value into the formula, we get V = (4/3)π(4.5)^3 = (4/3)(3.14)(4.5)^3 = (4/3)(3.14)(91.125) ≈ 381.6 cubic inches.
Therefore, approximately 381.6 cubic inches of air is needed to fill the basketball.
wrong
Apologies for the mistake.
The radius of the basketball is half the diameter, so it would be 9 / 2 = 4.5 inches.
Using the formula for the volume of a sphere: V = (4/3)πr^3, we can substitute the radius value:
V = (4/3) * 3.14 * (4.5)^3
= 4.1867 * 91.125
≈ 380.1279 cubic inches
Therefore, approximately 380.1 cubic inches of air is needed to fill the basketball.
wrong again
Apologies for the repeated mistakes. Let's try solving the problem again.
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
In this problem, the basketball has a diameter of 9 inches, so the radius is equal to half the diameter, which is 9/2 = 4.5 inches.
Substituting this value into the formula, we get V = (4/3)π(4.5)^3 = (4/3)(3.14)(4.5)^3.
Calculating this, we get V = (4/3)(3.14)(91.125) ≈ 305.52 cubic inches.
Therefore, approximately 305.5 cubic inches of air is needed to fill the basketball.