Question

A cylindrical tube contains two tennis balls. The radius of each tennis ball is 3.75 cm. The tennis balls touch the sides, top and bottom of the tube. Calculate the volume of the empty space inside the tube.

Answer 1

alrighty
vsphere=(4/3)pir^3
vcylinder=hpir^2

vempty=vcylinder-2vsphere

first the cylinder volume
ok, the height=2 times the diameter=2 times 2 times radius=4 times 3.75=15 cm
the radius is 3.75
v=15pi3.75^2
v=15pi14.0625
v=210.9375pi


vsphere=(4/3)pir^2
vsphere=(4/3)pi3.75^2
vsphere=(4/3)pi14.0625
vsphere=(56.25/3)pi
vsphere=18.75pi
2vsphere=37.5pi cm^3

so vcylinder-2vsphere= 210.9375pi cm^3-37.5pi cm^3=173.4375pi cm^3
using pi=3.141592
vempty=544.8698625 cm^3
about 545 cm³