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.
(1 point)
Responses
113 in.3
113 inches cubed
3,052.1 in.3
3,052.1 inches cubed
190.8 in.3
190.8 inches cubed
381.5 in.3
113 cubic inches
Given the diameter of 9 inches, the radius would be 4.5 inches. The formula for the volume of a sphere is V = (4/3) * pi * r^3. Plugging in the values, V = (4/3) * 3.14 * 4.5^3 = 113.04 cubic inches. Rounded to the nearest tenth, this becomes 113 cubic inches.
incorrect
I apologize for the mistake. Let's re-calculate the volume using the correct formula and check the options again.
Given diameter = 9 inches, radius (r) = 4.5 inches.
The formula for the volume of a sphere is V = (4/3) * pi * r^3.
Substitute the values:
V = (4/3) * 3.14 * 4.5^3
V ≈ (4/3) * 3.14 * 91.125
V ≈ 4.1888 * 91.125
V ≈ 381.4725 cubic inches
Rounded to the nearest tenth, the volume needed to fill the basketball is 381.5 cubic inches.
Therefore, the correct option is:
381.5 in.3
381.5 inches cubed