Question

six squash balls are packaged in a cylindrical container. Calculate the volume of air inside the container in terms of the radius r (Hint: volume of container minus volume of 6 squash balls

Answer 1

In order to fit 6 squash balls into a cylinder container, the radius r has to be the same for the ball and for the base of the cylinder, and the height h of the container must be equal to 6 diameters d or 12 radii of the ball. Volume of the ball and the container is:

Vb=(4/3)r³π, Vc=r²πh, h is the height of the cylindrical container.
h=12r.

So now the volume of the cylinder is:
Vc=r²π*12r=12r³π.

There are 6 balls so their total volume is:
6*Vb=6*(4/3)*r³*π=(24/3)*r³π=8r³π.

Now we subtract the volume of 6 balls from the volume of the cylinder to get the volume of air Va inside the cylinder:

Va=Vc-6*Vb=12r³π-8r³π=4r³π.

So the volume of air inside of the cylinder is Va=4r³π