# Thread: Can someone just explain this to me please?

1. ## Can someone just explain this to me please?

R is the region bounded below by y=x^2 and above by y=1. Suppose a solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of this solid.

I know the answer is 2 (I think), but can someone explain how to do this?

2. See attachment -- I get 16/15

3. Originally Posted by zhupolongjoe
R is the region bounded below by y=x^2 and above by y=1. Suppose a solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of this solid.

I know the answer is 2 (I think), but can someone explain how to do this?
I also get 2. Since you want the cross-sections to be perpendicular to the y-axis, it's probably best to look at this as a function of y. So we have $\displaystyle f(y)=\pm\sqrt{y}$.

Because the length of the square goes from $\displaystyle -\sqrt{y}$ to $\displaystyle \sqrt{y}$, the side length of each square is $\displaystyle \sqrt{y}-(-\sqrt{y})=2\sqrt{y}$. Thus the equation you want to integrate is:

$\displaystyle \int_0^1(2\sqrt{y})^2\,dy$

and this does come out to 2.

Calculus26's math is right, but in his post he has the side lengths parallel to the y-axis, not perpendicular, and this changes the answer.

4. Yeah I read it wrong was thinking perpindicular to the x axis