Question

Triangle ABC is a 45°-45°-90° triangle inscribed in a sphere such that B is the center of the sphere, and A and C are points on the sphere. Given the hypotenuse of ABC is 32 units, what is the surface area of the sphere?

Answer 1

If B is in the center of the circle, and A and C touch the circumference, then AB = BC = r. Using Pythagorean theorem, we get:

2r^2 = 32^2 or r^2 = (32^2)/2

Solve for r^2. Insert that value into the equation below and solve for A.

A = 4πr^2