Find the volume of a cylinder if its axial section is a square whose perimeter is 24 cm

A cylinder is a geometric body based on the rotation of a rectangle around its side.

The axial section of a cylinder is a plane passing through the axis, that is, through the center of its bases.

Since in a square all sides are equal, and the perimeter is 24 cm, the length of its sides is:

AB = BC = CD = AD = P / 4;

AB = BC = CD = AD = 24/4 = 6 cm.

Thus, the height of the cylinder and its diameter are equal to the length of the side of the axial section:

D = 6 cm;

H = 6 cm.

The volume of a cylinder is the product of its base area by its height. Since the base of the cylinder is a circle, the volume formula will look like this:

V = H * πR ^ 2, where:

V is the volume of the cylinder;

H – height;

R is the radius of the base;

The radius of the cylinder base is equal to half of its base:

R = D / 2;

R = 6/2 = 3 cm.

V = 6 * 3.14 * 32 = 6 * 3.14 * 9 = 169.56 cm3.

Answer: the volume of the cylinder is 169.56 cm3.