What should be the radius of the base of a cylinder with a square axial section

What should be the radius of the base of a cylinder with a square axial section, so that its lateral surface is the same as the surface of a ball with a radius of 1.5 cm.

First, we find the surface area of the ball, using the formula:

S = 4πr ^ 2;

S = 4π · 1.5 ^ 2 = 4π · 2.25 = 9π.

The lateral surface area of the cylinder is calculated by the formula:

S = 2πrh.

The cylinder is formed by rotating a rectangle around its side.

An axial section is a plane passing through the axis of a given cylinder.

Since the axial section of this cylinder is a square, then:

h = 2r;

S = 2πr ^ 2r = 4r ^ 2π;

4r ^ 2π = 9π;

r ^ 2 = 9π / 4π = 2.25;

r = √2.25 = 1.5 cm.

Answer: the radius of the base of this cylinder will be 1.5 cm.