A right circular cylinder having the radius of r and height of h is inscribed in a sphere. The sphere's diameter is D. What is the relationship between the height of the cylinder h and its radius r in terms of the sphere's diameter D?
Show answer & explanation
Correct answer: A
Explanation
Given:
Radius of the cylinder = r
Height of the cylinder = h
Diameter of the sphere = D
By the formula:
Radius of the sphere = D/2
r² + (h/2)² = (D/2)²
r² + h²/4 = D²/4
4r² + h² = D²
h² = D² − 4r²
h = √(D² − 4r²)