Question

alex wong basketball after making a half court shot. the display box for his new basketball is in the shape of a cube. alex measures the length of one side of the cube to be 9.5 inches. the basketball inside is touching every wall of the box. how many cubic inches of air is surrounding the ball in the box

Answer 1

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 diameter of the sphere = the side of the cube
• The empty volume of the cube is the difference between the volume of the cube and the volume of the sphere

∵ 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) =  $\frac{4}{3}$ π r³

∵ r = 4.75

∴ Volume the ball = $\frac{4}{3}$ (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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