My Math Forum help setting these up-slicing

 Calculus Calculus Math Forum

 January 29th, 2013, 08:36 AM #1 Member   Joined: Oct 2012 Posts: 94 Thanks: 0 help setting these up-slicing 31. The vertex of a pyramid lies at the origin, and the base is perpendicular to the x-axis at x=4. The cross sections of the pyramid perpendicular to the x-axis are squares whose diagonals run from the curve y=-5x^2 to the curve y=5x^2. 33. The base of a solid is the circle x^2 + y^2 = a^2. Each section of the solid cut by a plane perpendicular to the x-axis is a square with one edge in the base of the solid. Find the volume of the solid.
January 29th, 2013, 11:25 AM   #2
Math Team

Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: help setting these up-slicing

Quote:
 Originally Posted by cheyb93 31. The vertex of a pyramid lies at the origin, and the base is perpendicular to the x-axis at x=4. The cross sections of the pyramid perpendicular to the x-axis are squares whose diagonals run from the curve y=-5x^2 to the curve y=5x^2.
So the length of each diagonal is $5x^2- (-5x^2)= 10x^2$. Now, if a square has sides of length s, it has diagonals of length $s\sqrt{2}$. Setting that equal to $10x^2$, that is, $s\sqrt{2}= 10x^2$ so that . That means that each square has area
$s^2= 50x^4$. Taking each square to have "thickness" dx, it has volume $50x^4dx$ and integrating that from 0 to 4 will give the volume.

Quote:
 33. The base of a solid is the circle x^2 + y^2 = a^2. Each section of the solid cut by a plane perpendicular to the x-axis is a square with one edge in the base of the solid. Find the volume of the solid.
For given x, then, y goes from $-\sqrt{a^2- x^2}$ to $\sqrt{a^2- x^2}$, length of $2\sqrt{a^2- x^2}$. The square will have are $4(a^2- x^2)$.

That's all pretty standard. I am puzzled that you showed no attempt of your own.

 January 29th, 2013, 08:02 PM #3 Member   Joined: Oct 2012 Posts: 94 Thanks: 0 Re: help setting these up-slicing Our professor gave us one example on the board, only one homework problem on this topic, and there was very little instruction in the book. I am not sure why you are puzzled, but thanks anyway for helping.

 Tags setting, upslicing

,

,

,

,

### the vertex of a pyramid lies at the origin, and its base is perpendicular to the x axis at x = 4

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post cheyb93 Calculus 1 March 21st, 2013 05:58 PM cheyb93 Calculus 1 March 21st, 2013 12:15 PM cheyb93 Calculus 2 January 27th, 2013 08:15 PM Icarus Calculus 2 November 2nd, 2012 02:30 PM mathman2 Calculus 1 February 1st, 2010 03:30 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top