a plane is passed through a sphere at a point that is x units away from the center of a sphere. the radius of the sphere is y units.

Question

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

Answer 1

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