SOLUTION: A cylindrical can contains three tennis balls. The diameter of each tennis ball is 8cm. If the tennis balls fit snuggly against the interior of the can, and against the top and bot

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Question 212847: A cylindrical can contains three tennis balls. The diameter of each tennis ball is 8cm. If the tennis balls fit snuggly against the interior of the can, and against the top and bottom of the can, how many cubic centimeters of empty space are in the can? Express your answer in terms of pi.
Found 2 solutions by ankor@dixie-net.com, Fombitz:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A cylindrical can contains three tennis balls.
The diameter of each tennis ball is 8cm.
If the tennis balls fit snuggly against the interior of the can, and against
the top and bottom of the can, how many cubic centimeters of empty space are in the can?
Express your answer in terms of pi.
:
r = 8/2 = 4 cm, h = 3(8) = 24 cm
;
Empty space (E) = the vol of the cylinder - the vol of the 3 balls
:
E = pi%2A4%5E2%2A24 - 3%284%2F3%29%2Api%2A4%5E3
3's cancel
E = pi%2A16%2A24 - 4%2Api%2A64
:
E = 384%2Api+-+256%2Api
:
E = 128%2Api

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The cylindrical can has a length of 3*8=24 cm.
The diameter of the can is 8 cm.
The volume of the cylinder is
V=pi*(D/2)^2*(3D)=(3/4)*pi*D^3=384*pi
The three balls have a volume of
V=3*(4/3*pi*(D/2)^3)=(pi/2)*D^3=256*pi
Difference=(384-256)*pi=128*pi