The main section of the cylinder is a square, the area of which is 36cm ^ 2. Find the volume of the cylinder.

1. Find the side of a square if its area is 36 cm2:

S = a ^ 2 = 36;

a = √36 = 6 (cm).

2. According to the problem statement, a square with a side of 6 cm is the main section of the cylinder, therefore the height of the cylinder is h = a = 6 cm. And also the diameter of the circle, which is the base of the cylinder, d = a = 6cm. Find the radius of the circle:

r = d / 2 = 3 (cm).

3. The volume of the cylinder can be found by the formula V = Sb * h, where Sb is the area of the base, that is, the circle. Sop = nr ^ 2, (n = 3.14). Let’s calculate:

V = 3.14 * 3 ^ 2 * 6 = 678.24 (cm3).

Answer: the volume of the cylinder is 678.24 cm3.