408.454 cubic inches of air is surrounding the ball in the box
Step-by-step explanation:
When a sphere is inscribed in a cube and touching all of its faces, then
∵ The basketball is shaped a sphere
∵ The box is shaped a cube
∵ The ball touching every wall of the box
∴ The diameter of the ball = the side of the box
∵ The length of one side of the cube = 9.5 inches
∴ The diameter of the ball = 9.5 inches
∵ The diameter of the ball = 2 r, where r is the radius of the ball
∴ 9.5 = 2 r
- Divide both sides by 2
∴ r = 4.75 inches
∵ The volume of the air that surrounded the ball in the box =
volume of the box - volume of the ball
∵ Volume box (cube) = s³
∵ s = 9.5 inches
∴ Volume of the box = (9.5)³
∴ Volume of the box = 857.375 inches³
∵ Volume the ball (sphere) = [tex]\frac{4}{3}[/tex] π r³
∵ r = 4.75
∴ Volume the ball = [tex]\frac{4}{3}[/tex] (π)(4.75)³
∴ Volume the ball = 448.921 inches³
Substitute the values of the volumes of the box and the ball in the rule above
∴ The volume of the air = 857.375 - 448.921
∴ The volume of the air = 408.454 inches³
408.454 cubic inches of air is surrounding the ball in the box
Learn more:
You can learn more about volume of solids in brainly.com/question/12497249
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