Volume of Spheres Quick Check
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Question
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
381.5 in.3
381.5 inches cubed
113 in.3
113 inches cubed
190.8 in.3
190.8 inches cubed
3,052.1 in.3
The correct answer is 190.8 in.3.
Explanation:
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
Since the diameter of the basketball is 9 inches, the radius is half of that, so r = 4.5 inches.
Plugging this into the formula, we get V = (4/3)(3.14)(4.5)^3 = 190.8 in.3.
Therefore, 190.8 in.3 of air is needed to fill the basketball.