To find the area of a circular ring,
or space included between the circumferences of two circles, the one within the other.
1. Subtract the square of the less diameter from the square of the greater, and multiply their difference by ·7854.
2. Or, find the area of each circle separately, and subtract one from the other, for the area required.
3. Or, multiply the sum of the diameters by the difference of the same, and that product by ·7854 for the area.
Example.—Required the area of a ring, the diameters of whose bounding circles are 10, and 20.
By Rule 3.
20 + 10 = 30, sum of diameters.
20 - 10 = 10, difference of diameters.
30 × 10 × ·7854 = 235·62. The area.
To find the length of any arc of a circle.
1. As 360° is to the number of degrees in the arc, so is the circumference to the length of the arc.