## Circle or Sector

The area of a circle, in a slightly different form, was used in Chapter 5 in figuring engine displacement.

where A = Area; n = 3.14; r = Radius of the circle.

A sector is slice of a circle. The known dimensions, the angle or the arc length, dictate the equation used to solve for the area of the sector. Study Figure 13.13. When the angle is known, the equation for a sector is:

where A = Area; n = 3.14; 0 = Included angle of the sector; r = Radius of sector.

43,560 ft2 FIGURE 13.13. Circle and sectors.

When the length of the arc is known, the equation for a sector is:

r x arc length

Problem: Find the area of a circle (ft2) having a radius of 75.0 ft.

Solution:

A = n x r2 = 3.14 x (75.0 ft)2 = 17662.5 or 17,700 ft2

Problem: Find the area of a sector (ft2) having a radius of 135.0 ft and an angle of 60.0°.

Solution:

360 360

3,433,590 2

Problem: What is the area of a sector (ac) if the radius is 100.0 ft and the arc length is 210.0 ft?

Solution: (Adding the conversion value from square feet to acres):

2 43,560 ft2

2 43,560 ft2

21,000

87,120