Volume by Slicing: A cylindrical wedge, help needed please

[RolloJarvis]

Homework Statement

Find the volume of curved wedge that is cut from a cylinder of radius 3m by two planes. One plane perpendicular to the axis of the cylinder, the other plane crosses the first plane at a 45 degree angle at the centre of the cylinder.

(Hint: let the line of intersection of the two planes be the y-axis and then the cross section of the slice is a rectangle whose area you need to find as a function of x)

Homework Equations

V = \int^{b}_{a}A(x) dx

The Attempt at a Solution

I need to find the area of the rectangle described above as a function of x so i can integrate it to find the volume.

The length of the vertical sides of the rectangle will given by the function y=x/2, and i presume the horizontal sides would be some function involving sin, seeing as is starts at 0, ends at 0, and has a maximum or 2r in the middle of the cylinder... but i can't figure it out. this is the bit I am stuck on.

Thanks for the help!

 

[LCKurtz]

It's always a good idea to draw a picture. Maybe this will help

It isn't clear from your post whether you also want the back half, which would double the answer.

 

[RolloJarvis]

It's always a good idea to draw a picture. Maybe this will help

It isn't clear from your post whether you also want the back half, which would double the answer.

of course! that makes a lot more sense with the picture, out of curiosity, what program did you use to draw the diagram? I do a lot of lab reports and a good drawing package would be very useful.

I will post a new attempt at an answer when i get the chance.

in regards to the back half also, I am unsure as all the information i have been given is written above. i guess i will just write each half = ... explicitly on the answer sheet.

 

[LCKurtz]

of course! that makes a lot more sense with the picture, out of curiosity, what program did you use to draw the diagram? I do a lot of lab reports and a good drawing package would be very useful.

It's called Mayura Draw:

http://www.mayura.com/