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10.26. For a square, find the area in terms of p of the
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CHAPTER 10 Regular Polygons and the Circle
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(10.9)
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(a) Circumscribed circle if the length of the apothem is 7 (b) Circumscribed circle if the perimeter is 24 (c) Circumscribed circle if the length of a side is 8 (d) Inscribed circle if the length of the apothem is 5 (e) Inscribed circle if the length of a side is 12 22 (f) Inscribed circle if the perimeter is 80 10.27. Find the circumference and area of the (1) circumscribed circle and (2) inscribed circle of (a) A regular hexagon if the length of a side is 4 (b) A regular hexagon if the length of the apothem is 4 23 (c) An equilateral triangle if the length of the altitude is 9 (d) An equilateral triangle if the length of the apothem is 4 (e) A square if the length of a side is 20 (f) A square if the length of the apothem is 3 10.28. Find the radius of a pipe having the same capacity as two pipes whose radii are (a) 6 ft and 8 ft; (b) 8 ft and 15 ft; (c) 3 ft and 6 ft. (Hint: Find the areas of their circular cross-sections.) (10.10) 10.29. In a circle, find the length of a 90 arc if (a) The radius is 4. (b) The diameter is 40. (c) The circumference is 32. (d) The circumference is 44p. (e) An inscribed hexagon has a side of length 12. (f) An inscribed equilateral triangle has an altitude of length 30. 10.30. Find the length of (a) A 90 arc if the radius of the circle is 6 (b) A 180 arc if the circumference is 25 (c) A 30 arc if the circumference is 60p (d) A 40 arc if the diameter is 18 (e) An arc intercepted by the side of a regular hexagon inscribed in a circle of radius 3 (f) An arc intercepted by a chord of length 12 in a circle of radius 12. 10.31. In a circle, find the area of a 60 sector if (a) The radius is 6. (b) The diameter is 2. (c) The circumference is 10p. (d) The area of the circle is 150p. (e) The area of the circle is 27. (f) The area of a 240 sector is 52. (g) An inscribed hexagon has a side of length 12. (h) An inscribed hexagon has an area of 24 23. (10.12) (10.11) (10.11) (10.9)
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CHAPTER 10 Regular Polygons and the Circle
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10.32. Find the area of a (a) 60 sector if the radius of the circle is 6 (b) 240 sector if the area of the circle is 30 (c) 15 sector if the area of the circle is 72p (d) 90 sector if its arc length is 4p
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(10.12)
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10.33. Find the measure of a central angle of an arc whose length is (a) 3 m if the circumference is 9 m (b) 2 ft if the circumference is 1 yd (c) 25 if the circumference is 250 (d) 6p if the circumference is 12p (e) Three-eighths of the circumference (f) Equal to the radius
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(10.12)
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10.34. Find the measure of a central angle of a sector whose area is (a) 10 if the area of the circle is 50 (b) 15 cm2 if the area of the circle is 20 cm2 (c) 1 ft2 if the area of the circle is 1 yd2 10.35. Find the measure of a central angle of (a) An arc whose length is 5p if the area of its sector is 25p (b) An arc whose length is 12p if the area of its sector is 48p (c) A sector whose area is 2p if the length of its arc is p (d) A sector whose area is 10p if the length of its arc is 2p 10.36. Find the radius of a circle if a (a) 120 arc has a length of 8p (b) 40 arc has a length of 2p (c) 270 arc has a length of 15p (d) 30 sector has an area of 3p (e) 36 sector has an area of 21p 2 (f) 120 sector has an area of 6p (d) 5p if the area of the circle is 12p (e) Eight-ninths of the area of the circle
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(10.12)
(10.11 and 10.12)
(10.11 and 10.12)
10.37. Find the radius of a circle if a sector of area (a) 12p has an arc of length 6p (b) 10p has an arc of length 2p (c) 25 cm2 has an arc of length 5 cm (d) 162 has an arc of length 36
(10.12)
10.38. Find the area of a segment if its central angle is 60 and the radius of the circle is (a) 6; (b) 12; (c) 3; (d) r; (e) 2r. (10.13) 10.39. Find the area of a segment of a circle if (a) The radius of the circle is 4 and the central angle measures 90 . (b) The radius of the circle is 30 and the central angle measures 60 . (c) The radius of the circle and the chord of the segment each have length 12. (d) The central angle is 90 and the length of the arc is 4p. (e) Its chord of length 20 units is 10 units from the center of the circle. 10.40. Find the area of a segment of a circle if the radius of the circle is 8 and the central angle measures (a) 120 ; (b) 135 ; (c) 150 . (10.13) (10.13)