Plane trigonometry, by S.L. Loney.

AREA OF A CIRCLE.

267. area of sector AOB = x area of whole circle
1r7
- x rR2- R. a.
27r 2
EXAMPLES. XLI.
1. Find the area of a circle whose circumference is 74 feet.
2. The diameter of a circle is 10 feet; find the area of a sector whose
arc is 220~.
3. The area of a certain sector of a circle is 10 square feet; if the
radius of the circle be 3 feet, find the angle of the sector.
4. The perimeter of a certain sector of a circle is 10 feet; if the
radius of the circle be 3 feet, find the area of the sector.
5. A strip of paper two miles long and '003 of an inch thick is rolled
up into a solid cylinder; find approximately the radius of the circular ends
of the cylinder.
6. A strip of paper, one mile long, is rolled tightly up into a solid
cylinder, the diameter of whose circular ends is 6 inches; find the thickness of the paper.
7. Given two concentric circles of radii r and 2r; two parallel
tangents to the inner circle cut off an arc from the outer circle; find its
length.
8. The circumference of a semicircle is divided into two arcs such
that the chord of one is double that of the other. Prove that the sum of
the areas of the two segments cut off by these chords is to the area of the
semicircle as 27 is to 55.
[- 22 ]
[7r4
9. If each of 3 circles, of radius a, touch the other two, prove that
4the area included between them is nearly equal to
the area included between them is nearly equal to a2.