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Name the minor arc and find its measure.

1. Name the minor arc and find its measure. Hint #. 1. A minor arc is less than a semicircle The measure of an arc is equal to its central angle. Name the major arc and find its measure. 2. Hint #. 2. A major arc is greater than a semicircle. Find the measure by subtracting from 360°.

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Name the minor arc and find its measure.

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  1. 1 Name the minor arc and find its measure.

  2. Hint # 1 • A minor arc is less than a semicircle • The measure of an arc is equal to its central angle.

  3. Name the major arc and find its measure. 2

  4. Hint # 2 • A major arc is greater than a semicircle. • Find the measure by subtracting from 360°.

  5. Identify a semicircle that contains C. 3

  6. Hint # 3 • A semicircle is half of a circle.

  7. 4 Find the length of arc XPY. Leave your answer in terms of π.

  8. Hint # 4 • Use the formula • m = 360 - m

  9. Find the area of the figure to the nearest tenth. 5

  10. Hint # 5

  11. Find the area of a sector with a central angle of 180° and a diameter of 5.6 cm. Round to the nearest tenth. 6

  12. Hint # 6

  13. Find the exact area of the shaded region. Leave in terms of π. 7

  14. Hint # 7 • Find the area of the sector • Find the area of the triangle (it is a 30-60-90) • We did this one in our notes

  15. 8 Find the area of the shaded region. Leave your answer in terms of π and in simplest radical form.

  16. Hint # 8 • Area of circle – area of triangle • Drop a perpendicular to create a 30-60-90 special right triangle

  17. 9 What is the probability that a point chosen at random on the grid will lie in the unshaded region?

  18. Hint # 9 • Probability = # of unshaded squares / total # squares

  19. 10 The radius of the bull’s-eye of the dartboard is 8 inches. The radius of each concentric circle is 8 inches more than the radius of the circle inside it. If a dart lands at random on the dartboard, what is the probability that the dart will hit in area C?

  20. Hint # 10 • Find the area of the largest circle (D) • Find the area of just C • Find the area of the circle with C and subtract the area of the circle with B • Divide the area of C by the area of D

  21. 11 A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 35 cm. To the nearest tenth, what is the area of the wheel?

  22. Hint # 11 • The distance they traveled with the wheel is the circumference of the circle.

  23. 12 Find the probability that a point chosen at random will lie in the shaded area.

  24. Hint # 12 • Find the area of the circle • Find the area of the triangle (the base is the diameter of the circle and the height is the radius of the circle). • Divide the area of the triangle by the area of the circle

  25. 13 A 4-ft-by-5-ft dock is anchored in the middle of a lake. The bow of a boat is tied to a corner of the dock with a 5-ft rope as shown in the picture. Find the area of the region in which the bow of the boat can travel. Round your answer to the nearest foot.

  26. Hint # 13 • The boat can travel ¾ of a circle with radius 5 feet, and then a quarter circle with radius 1 foot.

  27. The circumference of a circle is 60πcm. Find the diameter, the radius, and the length of an arc of 140°. 14

  28. Hint # 14 • Use the formula for circumference to solve for diameter • Use the diameter to find the radius and arc length

  29. 15 The figure represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Round to the nearest tenth.

  30. Hint # 15 • Find the area of the large circle (r = 5.4/2 +2.2) • Subtract the area of the inside circle (r = 5.4/2)

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