After using the ball for a game, the match referee, Jason, measured the ball’s radius and found it had decreased to 4.4 inches.The difference in the volumes before and after the match is 24.9 in^3.
If the given sphere is of radius r units, then its volume is given as:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]
The radius of a fully inflated soccer ball is 4.5 inches.
After using the ball for a game, the match referee, Jason, measured the ball’s radius and found it had decreased to 4.4 inches.
The initial volumes of ball is:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]
[tex]V= \dfrac{4}{3}\times\pi \times 4.5^3 \: \rm unit^3\\\\\\V = 121.5\pi[/tex]
The volume of the ball after the match
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]
[tex]V= \dfrac{4}{3} \pi 4.4^3 \: \rm unit^3\\\\V = 340.7\pi[/tex]
The difference in the volumes before and after the match
Vf-Vi = 24.9 in^3
So the ball lost about 24.9 in^3 of air during the match.
Learn more about the volume of a sphere here:
https://brainly.com/question/381274
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