My Math Forum Volume
 User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 August 26th, 2008, 01:27 PM #1 Newbie   Joined: Aug 2008 Posts: 1 Thanks: 0 Volume Hi, Let the volume D be: x >= 0 y >= 0 x²+y²<= 1 0<= z <= (x²-y²)/2 Compute the volum of D. Thx J.
August 27th, 2008, 01:18 PM   #2
Global Moderator

Joined: May 2007

Posts: 6,822
Thanks: 723

Re: Volume

Quote:
 Originally Posted by Jinx2 Hi, Let the volume D be: x >= 0 y >= 0 x²+y²<= 1 0<= z <= (x²-y²)/2 Compute the volum of D. Thx J.
This can be set up as an integral calculus problem, where the main problem is setting up the integration limits for x, y, and z. The integrand itself is 1.

Step 1: z integral = (x^2-y^2)/2
Step 2: set up the x,y integral. It will be a subset of the plane bounded by the x axis, the line y=x and the arc of the unit circle from the x axis to the y=x line. The figure looks like a pizza slice, 1/8 of a pie.
Step 3: convert the integral to polar coordinates. Then the domain of integral is r from 0 to 1 and t (angle) from 0 to pi/4.

I got an answer of 1/16.

 Tags volume

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Doc Algebra 2 October 30th, 2012 09:48 AM PedroMinsk Calculus 5 December 6th, 2010 03:05 AM PedroMinsk Calculus 0 December 3rd, 2010 12:03 PM canadianicon25 Calculus 3 August 22nd, 2009 09:23 AM zaidqais Calculus 3 May 3rd, 2009 03:47 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top