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
āµ The basketball is shaped a sphere
āµ The box is shaped a cube
āµ The ball touching every wall of the box
ā“ The diameter of the ball = the side of the box
āµ The length of one side of the cube = 9.5 inches
ā“ The diameter of the ball = 9.5 inches
āµ The diameter of the ball = 2 r, where r is the radius of the ball
ā“ 9.5 = 2 r
- Divide both sides by 2
ā“ r = 4.75 inches
āµ The volume of the air that surrounded the ball in the box =
Ā Ā volume of the box - volume of the ball
āµ Volume box (cube) = sĀ³
āµ s = 9.5 inches
ā“ Volume of the box = (9.5)Ā³
ā“ Volume of the box = 857.375 inchesĀ³
āµ Volume the ball (sphere) = Ā [tex]\frac{4}{3}[/tex] Ļ rĀ³
āµ r = 4.75
ā“ Volume the ball = [tex]\frac{4}{3}[/tex] (Ļ)(4.75)Ā³
ā“ Volume the ball = 448.921 inchesĀ³
Substitute the values of the volumes of the box and the ball in the rule above
ā“ The volume of the air = 857.375 - 448.921
ā“ The volume of the air = 408.454 inchesĀ³
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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