A sphere with radius 17 m is cut by a plane that is 8 m below its center Which is the best approximation of the area of the circle formed by the intersection of the plane and the sphere?

Answer 1

If you view the plane edge-on so that it appears as a line cutting through the sphere which appears as a circle, you can create a right triangle from the circle's center point down to the closest point on the line, then along the line to one of the points where it intersects the circle. The leg of the triangle going down from the center point is 8 meters long. The hypotenuse of the triangle, running from the circle's center to the point of intersection at the circles edge, is the radius of the circle which is 17 m.

We can now calculate the remaining leg of this right triangle (side 1 squared + side 2 squared = hypotenuse squared) as 82+x2 = 172 so x = 15. This leg of the triangle is half the length of the line segment within the circle, or going back to 3 dimensions, it is the radius of the circle created by the plane passing through the sphere.

The area of this circle is therefor pi * r2 where r = 15 so the area is approximately 707.