SOLUTION: Can Someone please help me, it would be greatly appreciated. A Plane passes 10cm from the center of a sphere forming a circle with radius 10cm. What is the radius of the sphere?

Algebra ->  Bodies-in-space -> SOLUTION: Can Someone please help me, it would be greatly appreciated. A Plane passes 10cm from the center of a sphere forming a circle with radius 10cm. What is the radius of the sphere?      Log On


   

Question 85403: Can Someone please help me, it would be greatly appreciated.
A Plane passes 10cm from the center of a sphere forming a circle with radius 10cm. What is the radius of the sphere?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
if you look at a cross section of the sphere that cuts through the center of the 10cm circle, you will see a circle with a flat spot (chord)

the chord is 20cm long (the diameter of the 10cm circle) and the distance from the center of the circle to the chord is 10cm

a line from one end of the chord to the center of the circle forms the hypotenuse of an isosceles right triangle - this is the radius of the sphere

the legs of the triangle are the distance from the center of the circle to the chord and half the length of the cord

by Pythagoras, the length of the hypotenuse is sqrt%2810%5E2%2B10%5E2%29 or 10+%28sqrt%282%29%29 ... this is the radius of the sphere