Question

Use Cavalieri's principle to show that the volume of 2 cylinders, one normal and one slanted with the same base and height are the same.

Please explain step by step what you did.

Answer 1

this page explains it pretty well

the pic alone used is probably enough to see what's going on and why it works

http://en.wikipedia.org/wiki/Cavalieri%27s_principle

Answer 2

yea i understand the picture but im not sure how to put it in words lol

Answer 3

in the pic, they used pennies

the individual pennies themselves take up the same volume

Answer 4

moving the pennies around will NOT change the volume of the individual pennies

Answer 5

so if a stack of 20 coins takes up some volume (say 100 cubic cm, just some random number being thrown out there)

then you can shift the stack around however you like and the total volume will always be 100 cc since the individual volumes do not change

Answer 6

if you take this example to the extreme, and you subdivide a cylinder into infinitely thin disks, then you can show that the volumes of a right cylinder and an oblique cylinder are the same (as long as the base area and height are the same)

Answer 7

ahh i see thanks a lot

Answer 8

yw