A sphere and a right circule cylinder of the same radius have equal volume. By what percentage does the diameter of the cylinder exceed its height ?

Explanation

Let the given sphere and cylinder have same radius r and let the height of the cylinder be h. Then,
volume of sphere = volume of cylinder
`rArr (4)/(3) pi r^(3) = pi r^(2)h`
`rArr r == (3h)/(4) rArr 2r = (3h)/(2) rArr d = (3h)/(2)`, where d is the diameter of the cylinder.
Thus, the diameter of the cylinder is `(3h)/(2)`
Excess of diameter of cylinder over its height =`((3h)/(2) - h) = (h)/(2)`
Excess % `= ((h)/(2) xx (1)/(h) xx 100%) = 50%`