Question

Six squash balls are packaged in a cylindrical container. Calculate the volume of air inside the container.

Answer 1

You can do this for the space around one ball, and then multiply the answer by 6.

Then the problem reduces to comparing the volume of a cylinder to one of a sphere, when they have the same diameter (and the height of the cylinder is the diameter of the ball).

Answer 2

Volume of cylinder of radius r: V = pi r^2 h.

Volume of cylinder whose height is 2r: V = pi r^2 (2r) = 2 pi r^3.

Volume of sphere or radius r: (4/3) pi r^3.

Answer 3

So the answer for one ball is 2 pi r^3 minus (4/3) pi r^3, or (2/3) pi r^3.

Multiply this by 6 and you're done.

Answer 4

(And note that above where I wrote "sphere or radius r" the "or" should be "of" -- sorry.)

Answer 5

its ok! Thank you!!

Answer 6

Did you get it? Did I lose you somewhere?

Answer 7

no I got it thank you :)

Answer 8

For one ball it is (2/3) pi r^3. For six it would be six times that, or 4 pi r^3.

So the answer is 4 pi r^3, where r is the radius of one ball (or the radius of the container).

Answer 9

yeah I got that answer Thanks a lot! :)

Answer 10

I don't know the radius of a squash ball offhand, sorry!