The formula for the cross-sectional area of a cylinder is given by the equation: A = πr², where A represents the area, π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circular base of the cylinder.
To understand why this formula works, let’s break it down: The cross-section of a cylinder taken perpendicular to its height is a circle. The area of a circle is calculated using the formula πr². Thus, when you have a cylinder, regardless of its height, the area of the cross-section remains constant as long as the radius stays the same.
For example, if a cylinder has a radius of 3 cm, you would calculate the cross-sectional area as follows: A = π(3 cm)² = π(9 cm²) ≈ 28.27 cm². This area tells you how much space is contained within one of the circular ends of the cylinder.