please help:
find the volume of a slice of the cylindrical cake of height 2 and radius 5 between the planes teta=pi/6 and teta=pi/3

Question

please help:
find the volume of a slice of the cylindrical cake of height 2 and radius 5 between the planes teta=pi/6 and teta=pi/3

terenzreignz · Answer

Let's just have the top-view of this cake, shall we?
|dw:1363000496904:dw|

terenzreignz · Answer

Just give me a go-signal if you want to proceed :)

anonymous · Answer

sure, lets do it...

terenzreignz · Answer

Just so we're clear, what's the volume of this entire cake?

anonymous · Answer

the volum of the entire cake should be   V=pi (R^2).h

terenzreignz · Answer

Yeah, so what is it?  You have a value for r and h, don't you? :)

anonymous · Answer

yes, but the problem is not to find the entire volum....it is the slice between  pi/3 and pi/6.......

terenzreignz · Answer

Yeah, as long as you have the volume, we can proceed.  Knowing the volume of the entire cake will give you an intuitive idea on the answer... ;)

anonymous · Answer

we have to use tripple integral.........I got 50pi/12....I don't knoe if this is right or not?

terenzreignz · Answer

Triple Integrals?  That sucks :D
I was thinking, divide this plane, this is the pi/6 plane...
|dw:1363006138632:dw|

terenzreignz · Answer

And this is the pi/3 plane...
|dw:1363006184021:dw|

terenzreignz · Answer

Now we need the volume of this slice..
|dw:1363006231376:dw|