Arc Length & Sector Area Problems
Learning Intentions and Success Criteria
- Use properties of circles to solve geometry problems arising from situations
- Use properties of circles to solve geometric problems and real-world problems
1) Find the arc length of arc AB and the sector area of sector ACB.
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2) Find the central angle.
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3) Find the central angle.
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4) The shaded area is 14π centimeters squared. Find the central angle.
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5) Find the radius.
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6) Find the radius.
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7) Find the radius of the minor sector with the area 382 square meters.
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8) Find the radius of the circle if the area of the shaded sector DEF is 50π square inches.
9) Miguel makes a pizza with pepperoni placed on the length of the crust of the entire circular pizza and placed more pepperoni in a concentric circle two-thirds away from the center of the pizza. He cuts a slice of pizza with a central angle of 68º to eat. The distance from the vertex of the pizza to the edge of its crust (radius) is 18 cm. a) Find the approximate length of the crust (arc) of the slice of pizza he cut to eat.
b) If there are 3 pepperoni on the length of the crust of the slice of pizza he cut, how many pepperoni slices are on two-thirds away from the center?
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10) Caroline is about to perform a relay handoff on a circular track. Her track partner, McKenna, is standing 93º away from her and she needs to run 9.74 meters in order to pass the baton to McKenna. What is the radius of the circular track?
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11) A lawn sprinkler located at the corner of a yard rotates through 90º and sprays water 30 ft. What is the area of the sector watered?
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12) A circular plot with a 720 ft diameter is watered by a spray irrigation system. To the nearest square foot, what is the area that is watered as the sprinkler rotates through an angle of 50?
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13) At a pizza restaurant, a personal pizza has a radius of 10 centimeters and costs $5. Another restaurant takes a pizza with radius 30 centimeters, cuts it into 8 slices of equal area, and charges $5 per slice. Which is a better deal? Explain your reasoning.