Computing Area of Two-dimensional Solids – Circles and Ellipses

in Aviation Mathematics

Circle

A circle is a closed, curved, plane figure. [Figure 1‑20] Every point on the circle is an equal distance from the center of the circle. The diameter is the distance across the circle (through the center). The radius is the distance from the center to the edge of the circle. The diameter is always twice the length of the radius. The circumference, or distance around, a circle is equal to the diameter times π.

Figure 1-20. Circle.

Figure 1-20. Circle.

Circumference = C = d π


The formula for the area of a circle is:

Area = π × radius2 = π × r2

Example: The bore, or “inside diameter,” of a certain aircraft engine cylinder is 5 inches. Find the area of the cross section of the cylinder.

First, substitute the known values in the formula:

A = π × r^2.

The diameter is 5 inches, so the radius is 2.5 inches. (diameter = radius × 2)

A = 3.1416 × (2.5 inches)^2 = 3.1416 × 6.25 square inches = 19.635 square inches

Ellipse

An ellipse is a closed, curved, plane figure and is commonly called an oval. [Figure 1-21] In a radial engine, the articulating rods connect to the hub by pins, which travel in the pattern of an ellipse (i.e., an elliptical or obital path).

Figure 1-21. Ellipse.

Figure 1-21. Ellipse.