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 radius of sphere= r= Radius of a right circular cylinder
According to the question,
Volume of cylinder= volume of a sphere
`rArr " "pir^(2) h = (4)/(3) pir^(3) rArr h = (4)/(3) r`
`because` Diameter of the cylinder = 2r
`therefore`Inreased diameter from height of the cylinder `= 2r-(4r)/(3) = (2r)/(3)`
Now,percentage increase in diameter of the cylinder `= (((2r)/(3) xx100))/((4)/(3)r) = 50%`
Hence, the diameter of the cylinder exceeds its height by 50%.