Unformatted text preview: Area of a Sector • Section 4.3 99 6. Find the area enclosed by the ﬁgure eight in Exercise 8 from Section 4.2.
For Exercises 79, ﬁnd the area of the sector for the given radius r and arc length s.
7. r = 5 cm, s = 2 cm 8. r = a, s = a 9. r = 1 cm, s = π cm For Exercises 1012, ﬁnd the area of the segment formed by a chord of length a in a circle of radius r .
10. a = 4 cm, r = 4 cm 11. a = 1 cm, r = 5 cm 12. a = 2 cm, r = 5 cm 13. Find the area of the shaded region in Figure 4.3.7.
7 4 8 3
5 9
6 6 5
Figure 4.3.7 Exercise 13 Figure 4.3.8 Exercise 14 Figure 4.3.9 Exercise 15 14. Find the area of the shaded region in Figure 4.3.8. (Hint: Draw two central angles.)
15. Find the area of the shaded region in Figure 4.3.9.
16. The centers of two circles are 4 cm apart, with one circle having a radius of 3 cm and the other a
radius of 2 cm. Find the area of their intersection.
17. Three circles with radii of 4 m, 2 m, and 1 m are externally tangent to each other. Find the area
of the curved region between the circles, as in Figure 4.3.10. (Hint: Connect the centers of the
circles.)
1 r
4 2 r Figure 4.3.10 Exercise 17 Figure 4.3.11 r Exercise 18 18. Show that the total area enclosed by the loop around the three circles of radius r in Figure 4.3.11
is (π + 6 + 3) r 2 .
19. For a ﬁxed central angle θ , how much does the area of its sector increase when the radius of the
circle is doubled? How much does the length of its intercepted arc increase? ...
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Arc Length

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