Determine the area of the axial section of the cylinder if it has the shape of a square, and the radius

Determine the area of the axial section of the cylinder if it has the shape of a square, and the radius of the base of the cylinder is 3 cm.

The axial section of a cylinder is a plane that passes through the axis of symmetry of the cylinder (the segment connecting the centers of the circles at the bases of the cylinder). Thus, the axial section of the cylinder can be either a rectangle or a quadrangle, the sides of which are equal to the diameter of the circle at the base and the generatrix of the cylinder.
Since the radius (r) of the base of the cylinder is 3 cm, the diameter (d) is:
d = 2 * r = 2 * 3 = 6 (cm).
Thus, the axial section of the cylinder given by the condition is a square with a side length of 6 cm.Since all sides of the square are equal, its area is found by the formula:
S = a²,
where a is the length of the side of the square.
Let’s find the area of ​​the axial section:
S = 6² = 36 (cm²).
Answer: S = 36 cm².