SOLUTION: A ball with a 22-in. circumference is tightly packed into a cubical box for shipment. (Round your answers to the nearest whole number.) (a) What is the volume of the ball?

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Question 925258: A ball with a 22-in. circumference is tightly packed into a cubical box for shipment. (Round your answers to the nearest whole number.)
(a) What is the volume of the ball?
in3
(b) What is the smallest possible volume for the box?
in3
(c) What percent of the space in the box is occupied by the ball?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A ball with a 22-in. circumference is tightly packed into a cubical box for shipment. (Round your answers to the nearest whole number.)
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Find the diameter of the ball::
pi*d = 22
diameter = 22/pi inches
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(a) What is the volume of the ball in cubic inches?
V = (4/3)pi*r^3 = (4/3)pi*(11/pi)^3 = (1774.67)/pi^2 in^3
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(b) What is the smallest possible volume for the box? in3
V = s^3 = (22/pi)^3 = 10648/pi^3 in^3
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(c) What percent of the space in the box is occupied by the ball?
[(4/3)pi*(11/pi)^3 / (22/pi)^3 = [(4/3)*11^3/p^2]/(22/pi)^3)
= [(4/3)*11^3*pi/22^3] = 52.36%
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Cheers,
Stan H.
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