Thread: Rotational Vol Question.

I´ll try to explain this problem. Trying to solve this for the last 40minutes now.


Equation: y = x^(0,5)

The area under this equation starts to rotate around the X-axis and gives you the rotational Volume (B).

When calculating the above mentioned volume: Int: from (a = 0) to (b), There is a line from the point b parallell to the X-axis ( called line d), that line crosses the y-axis. The area between: Y-axis; This line (d), and the area "above" the y = x^0,5 graph starts to rotate around the y axis. This gives you volume (A).

Find x when these areas have the same volumes ( A = B).

The equation for calculating volume rotating around X-axis is:
INT: (pi)*(y^2):dx from a to b (on the x-axis as limes a = 0)

The equation for calculating volume rotating around y-axis is: Int:2*pi*xy:dx from a to b (on the X-axis ALSOOO).

At first I thought, never mind the rotation, just solve so the areas a equal, but that was not very clever, points further from the axises give larger values for volume then closer points do.

I keep getting the answer x = 0,625^2 but that is wrong, THE CORRECT SOLUTION IS (6.25;2.5)
Hope I discribed this problem understandably.

It's a little difficult following what you mean - partly because you talk about the "area" of A whereas I think you mean "volume," and also because I don't know what the "a" value is supposed to signify. Is "a" = 0? And when you ask for the value of x, do you mean the value of b to make the two volumes equal?

I will assume that the problem is to find a value for b such that the volume B (which is the defined by rotating y = sqrt(x) about the x axis, and finding the volume from x = 0 to x = b) is equal to the volume A (defined as rotating y = sqtr(x) about the y axis, and finding the volume from y = 0 to y = sqrt(b). If I have that right, then the answer for b turns out to be 6.25. I can help you thorugh this, but before I do please verify that I have interpreted the problem correctly.

Yes, you are correct, my mistake talking about the areas when the question was about volume. Please How did you get the answer?

Given the function y = sqrt(x): the volume of B is:



The volume of A is:


Set volume A = volume B, and solve for the value of b.

That was nice and simple