Thread: Can't figure out how a area forumla was derived for a Slicing Method problem

Hi, new poster here, so please forgive any mistakes of mine.
I've been trying to solve this problem : "The solid with a semicircular base of radius 5 whose cross sections perpendicular to the base and parallel to the diameter are squares."
in an effort to study for an upcoming test I have.

My problem comes down to finding A(x) which I figured would be an area of a square, who's side length is equal to the formula for a semi circle or B - \sqrt{r^2 - (x - A)^2}, which ends up to be \sqrt{25 - x^2} right if the semi circle is centered on (0,0)? Well I went to check to see and the answer they had was 2\sqrt{25-x^2}.

The question is, where the heck did that 2 come from? Because for the life of me I can't reason where it came from.

Thanks in advance for any help

You must get a better relationship with symmetry.

Integation is on [-5,5] as you have it.

Due to symmetry, this is equivalent to twice the value of integration on [0,5] still using hte argument as you have it.