# The axial section area is 21 cm squared base area 18п cm squared find the volume of the cylinder

Axial section of a cylinder – a section of a cylinder by a plane that passes through the axis of rotation.

That is, the section will be a rectangle, whose vertical side is the height of the cylinder, which lies on the lateral surface of the cylinder, and the horizontal bottom side is the diameter of the cylinder base.

We know the cross-sectional area. Let’s find its side, which lies at the base of the cylinder.

The base of the cylinder is a circle. We find the area of the circle by the formula S = πr².

18π = π * r²;

r² = 18π: π;

r² = 18.

r = √18.

Find the height of the cylinder:

21 = 2√18 * height;

height = 21: 2√18.

Find the volume of the cylinder:

21: 2√18 * 18 = (21 * √ (9 * 2)): 2 = (21 * 3√2): 2 = 63√2 / 2 (cm²).

ANSWER: 63√2 / 2 (cm²).