If the volume of a sphere is equal to that of a cylinder having the same radius, then find the ratio of the radius to the height of the cylinder.
Answer & explanation
Correct answer: option 3
We know that,
The volume of a sphere = \(\frac{4}{3}\) × π × (radius)3
The volume of a cylinder = π × (radius)2 × (height)
Radius of sphere = radius of cylinder = r
Also, the height of the cylinder = h
So, \(\frac{4}{3}\) × π × r3 = π × r2 × h
= \(\frac{4}{3}\) × r = h
= \(\frac{r}{h}\) = \(\frac{3}{4}\)