- #1
ciubba
- 65
- 2
Homework Statement
Find the volume of the solid whose base is a 4 by 4 square. Cross sections perpendicular to one diagonal of the square base are semi-circles with diameter on the base.
Homework Equations
V=pi r^2
A=S^2
The Attempt at a Solution
The cross sections are perpendicular to the x axis, so I need to integrate with respect to x. I centered the square base on a cartesian coordinate system and found via the pythogorean theorem that half the diagonal, which I believe is the radius of the semicircle, has a value of 2*2^(1/2). V=pi r^2, so [tex] \int_{0}^{4}(pi*(2\sqrt{2})^2) dx[/tex] =100.53
Am I on the right track with this solution?