How long is a chord of a sphere that connects orthogonal radii of 8”? Explain and Leave your answer in simplest radical form.

Question

How long is a chord of a sphere that connects orthogonal radii of 8”? Show all your calculations and an explanation as to whether or not your answer is reasonable. Leave your answer in simplest radical form.

Answer 1

Orthogonal radii form a right angle where they meet. The chord connects the endpoints of the radii and forms the hypotenuse of a right triangle with the radii forming the legs. So you have a right triangle with each of the two legs being 8 inches long. Use the Pythagorean Theorem to find the length of the chord (hypotenuse).