Question

A sphere has radius 6 inches .What is the radius, in inches,of the

circle formed by the intersection of the sphere and a plane 3 inches from
the sphere's centre

Answer 1

Plane AB intersects the sphere at a distance of 7″ from center O.

Let r be the radius at the intersection of plane and sphere.

Area at the intersection = πr²

Given area at the intersection = 576π

πr² = 576π

r² = 576

Let R be the radius of the sphere.

R² = r²+7²

R² = 576+49

R= 25

Volume of the sphere = (4/3)πR³ = (4/3)π(25)³ = 65449.85

Ans: 65449.85 in³