express the cross_sectional area of intersection in terms of x and y

Hi Jennie,

When a plane passes through a sphere, the resultant cross section formed is a circle. If you try to think over it, you can easily deduce the radius of that circle as Square-root(y^2-x^2) ( Try thinking it as a right triangle with hypotenuse y unit and
the other two sides as x and the radius of the cross-sectional circle)

Therefore the cross-sectional area will be π*(y^2-x^2) as area of a circle with radius r is π*r^2