To boost sales, the president of Slirpy Soups decided to change the size of its cylindrical soup can by doubling one dimension and halving the other. Not knowing wich dimension to double and which to halve, the production people created cans of both types; they made cans with doubled heights and halved radii and they made cans with halved heights and doubled radii. How did the volume of the new cans compare with the original?
Original cylinder volume:
πr^2h
Doubled height, halved radius cylinder volume:
π(r/2)^2(2h)
= π(r^2/4)(2h)
= πr^2h/2
Therefore, this one is half the volume of the original cylinder.
Halved height, doubled radius cylinder volume:
...you try this one...