12-2 Area of Circles. Find the area of each circle. Round to the nearest tenth. 1. ANSWER: m 2. ANSWER: 12.6 yd 2 ANSWER: 132.
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1 Find the area of each circle. Round to the nearest tenth A motion detector at the corner of a building can detect motion outside within a radius of 20 feet as shown. Within what area can it detect motion? Round to the nearest tenth m yd ft 2 7. May is making doughnuts. First she cuts out a circle of dough with a diameter of 8 centimeters. Then she cuts a hole in the middle with a diameter of 3 centimeters. What is the area of the top of the doughnut? Round to the nearest tenth cm 2 Find the area of each circle. Round to the nearest tenth ft 2 4. radius = 3.6 kilometers 40.7 km 2 5. diameter = 10.5 centimeters 86.6 cm cm in 2 esolutions Manual - Powered by Cognero Page 1
2 diameter = yards yd mi ft radius = miles 42.2 mi Each shelf of a shelving unit is a quarter circle with a radius of 32 centimeters. What is the area of each shelf? Round to the nearest tenth cm Lauren has a sprinkler positioned in her lawn that directs a 12-foot spray in a circular pattern. About how much of the lawn does the sprinkler water if there is a rectangular flower bed 3 feet by 6 feet that is also in the path of the spray? 66.5 cm m ft What is the area of the CD shown below? Round to the nearest tenth. 14. radius = 9.6 feet ft diameter = 24.8 meters m cm 2 esolutions Manual - Powered by Cognero Page 2
3 21. The trunk of the General Sherman Tree in Sequoia National Park has a circumference of feet. If the tree were cut down at the base, what would be the area of the cross section? ft What is the diameter of a circle if its area is 35.6 square centimeters? Round to the nearest tenth. 6.7 cm 23. Find the radius of a circle if its area is 50 square inches. Round to the nearest inch. 4 in. Find the distance around and the area of each figure. Round to the nearest tenth. 24. semicircle 27. Multiple Representations In this problem, you will investigate the area of a circle as the radius changes. a. Table Make a table like the one shown. Find the area of each circle to the nearest tenth. b. Analyze Describe how the area of a circle changes when the radius is doubled. c. Logic Predict the area of a circle that has a radius of 96 centimeters. Explain your reasoning. Then verify your prediction by finding the area. a mm; 25.1 mm semicircle 25.7 ft; 39.3 ft quarter circle 17.9 in.; 19.6 in 2 b. The area is multiplied by 4. c. Sample answer: Since 96 = 48 2, the area should be or about 28,952.8 cm 2 ; actual area 28,952.9 cm Identify Structure The circular radio signal from transmitter A has three times the radius of the circular signal from transmitter B. How many times greater is the area of the signal from transmitter A than from transmitter B? Explain your reasoning. 9 times greater; The radius is squared to find the area, so three times the radius yields 9 times greater. esolutions Manual - Powered by Cognero Page 3
4 29. Model with Mathematics Draw and label a circle that has an area between 800 square centimeters and 820 square centimeters. Label the length of the radius and state the area of the circle to the nearest tenth. Sample answer: cm Construct an Argument Describe the difference between the circumference and area of a circle and explain how the formulas for circumference and area of a circle are related. Circumference measures the distance around a circle and is given in units. Area measures the surface enclosed by the circle and is given in square units. The formulas for both measures involve π and the radius. The formula for circumference is C = 2πr and the formula for area is A = πr Building on the Essential Question Describe how you can find the area of a circle given the radius, diameter, or circumference. If you know the radius, substitute the value for r in A = πr 2. If you know the diameter, first divide by 2 to find the radius. Then substitute the value for r in A = πr 2. If you know the circumference, substitute the value for C in C = 2πr and solve for r to find the radius. Then substitute the value for r in A = πr Find the area of a circle with a diameter of 22 millimeters. Round to the nearest tenth. A mm 2 B mm 2 C mm 2 D 69.1 mm 2 A 35. A sprinkler is set to cover the area shown. Find the area of the grass being watered if the sprinkler reaches a distance of 10 feet. 31. Persevere with Problems The radius of circle B is 2.5 times the radius of circle A. If the area of circle A is 8 square yards, what is the area of circle B? 50 yd Be Precise If the measures of the area and circumference of a circle have the same numerical values, what is the radius of the circle? Explain. 2 units; if r = 2, then C = 2π(2) or 4π units and A = π (2) 2 or 4π units 2. F 47.1 ft 2 G ft 2 H ft 2 J ft 2 H esolutions Manual - Powered by Cognero Page 4
5 36. The Blackwells have a circular pool with a radius of 10 feet. They want to install a 3-foot sidewalk around the pool. What will be the area of the walkway? Find the area of each figure. 41. A ft 2 B ft 2 C ft 2 D ft m 2 A 37. Short Response The area of a circle is square centimeters. a. Write an algebraic expression in terms of A that could be used to find the radius of the circle. b. Find the radius to the nearest tenth. a. b cm Find the circumference of each circle. Round to the nearest tenth. 38. radius: 8 in cm in Find the product of and in. 39. radius: 12.5 ft 78.5 ft 40. diameter: 21 cm 66.0 cm Find each sum esolutions Manual - Powered by Cognero Page 5
6 Identify any equivalent expressions. 49. x + x 3x,, x x + x 3x and x (x 2), 2x 2, x(x 2) no equivalent expressions esolutions Manual - Powered by Cognero Page 6
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