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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.

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

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PIYUSH L. | Maths tutoring for middle school to college maths studentsMaths tutoring for middle school to coll...
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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