Question

Find the ratio of the volume of the cylinder to the volume of the hemisphere, given that the height,
h, of the cylinder is equal to the diameter, d, of the hemisphere

Answer 1

volume of cyl: pi r^2 h

but if h = d then h = 2r, so

pi * r^2 * 2r

= 2pi * r^3

Vol of hemisphere = (1/2) volume of sphere:

= 2/3 pi r^3

So the ratio is obvious from those results.