The height of the cylinder is 3 and the diagonal of the axial section is 5. Find the radius of the base.

A cylinder is a solid formed by rotating a rectangle around its side.

Thus, the axial section of the cylinder is rectangular. Let’s designate it AВСD.

The diagonal of the axial section divides it into two, equal to each other, right-angled triangles.

Consider a triangle ΔABС. Side AB is the height of the cylinder, BC is its diameter, AC is the diagonal of the axial section.

We can find the diameter of the base. To do this, apply the Pythagorean theorem:

AC ^ 2 = AB ^ 2 + BC ^ 2;

BC ^ 2 = AC ^ 2 – AB ^ 2;

BC ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16;

BC = √16 = 4 cm.

Since the radius of the base is half its diameter:

r = d / 2;

r = 4/2 = 2 cm.

Answer: The radius of the base of the cylinder is 2 cm.