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
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
Solution
The volume of a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere.
The volume of a cylinder is given by the formula πR²h, where R is the radius of the base of the cylinder and h is the height of the cylinder.
Given that the height of the cylinder is two times the base radius, we can substitute h = 2R in the cylinder volume formula to get πR²(2R) = 2πR³.
Since the volume of the sphere is equal to the volume of the cylinder (because the sphere is melted to form the cylinder), we can set the two volume formulas equal to each other and solve for R:
(4/3)πr³ = 2πR³
Divide both sides by π to get (4/3)r³ = 2R³.
Then divide both sides by 2 to get (2/3)r³ = R³.
Finally, take the cube root of both sides to get R = r*(2/3)^(1/3).
So, R is not equal to r. Therefore, option A is incorrect.
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