calculate the ratio of the area to the volume for a unit cube a unit sphere inscribed inside the cube and a right cylinder incribed inside the cube

Answer 1

Let the unit cube side be a. Its volume is a^3. Its area is 6a^2. The ratio is a/6.

The inscribed sphere has a volume of (pi/6)a^3 and an area of pi*(a/2)^2*4 = pi a^2. The ratio is a/6.

The inscribed right cylinder has a volume (pi/4)a^2*a = pi*a^3/4 and an area a*pi*a + 2 pi (a/2)^2
= (3/2) pi a^2
The ratio is a/6.

Interesting result