Question

A cylindrical canister contains three tennis balls. Assume the tennis balls touch the sides of the canister and the top and bottom with no gaps. If each ball is 2.7 inches in diameter, how much wasted space is in the canister? Round to the nearest hundredth.

Answer 1

Ok, so we know that teh diameters of the 3 tennis balls added up equals the height of the canister

also, since the tennis balls touch the sides, the diameter of the tennis ball=diameter of the base

so what we do is
canister volume-3tennisballvolume=wasted space

normally alot of the equations are using radius so
2.7=diameter
diameter=2r
d/2=r
2.7/2=r
1.35=r

since we are to aprox volume to hundreth. use 3.14=pi

volume of cylinder=hpir^2
volume of sphere (tennis ball)=volume of spere=$\frac{4}{3}pir^{3}$

first find volume of cylinder

h=3 times diameter of 1 tennis ball=3 times 2.7=8.1
r=1.35
vofcylinder=8.1 times 3.14 times 1.35^2
v=25.434 times1.8225
v=46.353465 (keep as many digits a possible for accuracy)


volume of tennis balls=volume of shpere times 3
v=$\frac{4}{3}pir^{3}$ times 3
and we can see that the 4/3 and the 3 cancel to get 4
v=$4pir^{3}$
v=$4pi1.35^{3}$
v=4(3.14)(2.460375)
v=30.90231


so we have
volume of canister=46.353465 in^3
volume of tennis balls=30.90231 in^3
subtract
wasted space=46.353465-30.90231
wasted space=15.451155
round to hundreth
15.45


wasted space=15.45 in^3