A sphere and a right cylinder have the same radius and volume. Find the radius r in terms of the height h of the cylinder.

Answer 1

The volume of a right cylinder is given by the formula C_V = pi x r² x h where r is the radius & h is the height

and the Vovume of a sphere is given by S_V = 4/3 x pi x r³

Equating the two formulas since the volumes are equal we have;

4/3 x pi x r³ = pi x r² x h Solving for h we have

h = 4/3 x r

Answer 2

V(cyl) = h*pi r^2.

V(sphere) = 4/3 pi r^3

Since the volumes are equal and the r's are equal:

h * pi * r * r = 4/3 * pi * r * r * r

Divide both sides by (pi * r * r) to get:

h = 4/3 r

or

r = 3/4 h