geometry

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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?

  • geometry -

    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

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