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. Ignoring the thickness of the materials the soccer ball is made from, find the volume of the ball before and after the match, and find the difference of the volumes before and after the match.

Question

Frederick Quinn

Mathematics

17 September, 02:37

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. Ignoring the thickness of the materials the soccer ball is made from, find the volume of the ball before and after the match, and find the difference of the volumes before and after the match.

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Coleman Dean · Answer 1

The volume of a sphere is:

V = (4pr^3) / 3 so the initial volumes is:

Vi = (4p*4.5^3) / 3=121.5p in^3 (before match, approx 381.7 in^3)

Vf = (4p*4.4^3) / 3=340.736p/3 (after match, approx 356.8 in^3

Vf-Vi=24.9 in^3

So the ball lost about 24.9 in^3 of air during the match ...