A solid metal sphere is melted and recast into a cylinder, where the radius of the cylinder is twice that of the sphere. If the height of the cylinder is h and the radius of the sphere is r, what is the ratio of h to r?
Show answer & explanation
Correct answer: B
Explanation
Given:
Sphere radius = r
Cylinder radius = 2r
Formula:
Volume of sphere = (4/3)πr³
Volume of cylinder = πR²h
Volume of sphere = Volume of cylinder
(4/3)πr³ = π(2r)²h
(4/3)πr³ = 4πr²h
(1/3)r = h
h : r = 1 : 3