A solid spherical metal ball is melted to form a solid right circular cylinder; whose height is two times that of base radius. If radii of the sphere and base of cylinder are r and R respectively, thenA R = r B C D
Question
A solid spherical metal ball is melted to form a solid right circular cylinder; whose height is two times that of base radius. If radii of the sphere and base of cylinder are r and R respectively, thenA R = r B C D
Solution
The question seems to be incomplete. However, I can provide a solution based on the information given.
Given that a solid spherical metal ball is melted to form a solid right circular cylinder, the volume of the sphere will be equal to the volume of the cylinder.
The volume of a sphere is given by (4/3)πr³ and the volume of a cylinder is given by πR²h, where r is the radius of the sphere, R is the radius of the base of the cylinder, and h is the height of the cylinder.
According to the problem, the height of the cylinder is two times the base radius, so we can substitute h = 2R in the cylinder volume formula.
So, we have:
(4/3)πr³ = πR²(2R)
Solving for R, we get:
R = r
So, the radius of the base of the cylinder is equal to the radius of the sphere, which corresponds to option A.
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