11-8 Area of Circles ANSWER: ANSWER: ANSWER: 4. radius = 3.6 kilometers ANSWER: 5. diameter = 10.5 centimeters ANSWER:
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1 Find the area of each circle. Round to the nearest tenth m 2 6. TRAMPOLINES An exercise trampoline has a diameter of 36 inches. a. Find the area of the trampoline. Compare to the estimate. b. The safety padding around the jumping surface is 4 inches wide. What is the area of the jumping surface? (Hint: Draw and label a diagram.) a. 1,017.9 in 2 ; Since 1, , the estimate is reasonable. b in 2 Find the area of each shaded sector. Round to the nearest tenth yd in ft 2 4. radius = 3.6 kilometers 40.7 km 2 5. diameter = 10.5 centimeters 86.6 cm m 2 Find the area of each circle. Round to the nearest tenth cm 2 esolutions Manual - Powered by Cognero Page 1
2 radius = 9.6 feet ft in diameter = 24.8 meters m diameter = yards yd mi radius = miles mi ft LAWN CARE 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? cm ft CDS What is the area of the CD shown below? Round to the nearest tenth m cm 2 esolutions Manual - Powered by Cognero Page 2
3 Find the area of each shaded sector. Round to the nearest tenth NATURE 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 m 2 Find the distance around and the area of each figure. Round to the nearest tenth. 28. semicircle mm; 25.1 mm ft The diameter of a circle is 6 millimeters. It has a sector with a central angle of 72. What is the area of the sector to the nearest tenth? 5.7 mm The diameter of a circle is 11 yards. It has a sector with a central angle of 20. What is the area of the sector to the nearest tenth? 5.3 yd Find the radius of a circle if its area is 50 square inches. Round to the nearest inch. 29. semicircle 25.7 ft; 39.3 ft quarter circle 17.9 in.; 19.6 in 2 4 in. 26. What is the diameter of a circle if its area is 35.6 square centimeters? Round to the nearest tenth. 6.7 cm esolutions Manual - Powered by Cognero Page 3
4 31. MULTIPLE REPRESENTATIONS In this problem, you will investigate the area of a circle as the radius changes. a. Tabular Make a table like the one shown. Find the area of each circle to the nearest tenth. 32. OPEN ENDED 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: b. Analytical Describe how the area of a circle changes when the radius is doubled. c. Logical 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 cm WRITING IN MATH 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 CHALLENGE 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? 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 yd REASONING 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. esolutions Manual - Powered by Cognero Page 4
5 36. WRITING IN MATH 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 38. A sprinkler is set to cover the area shown. Find the area of the grass being watered if the sprinkler reaches a distance of 20 feet. 39. 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? A ft 2 B ft 2 C ft 2 D ft 2 A 40. EXTENDED RESPONSE The area of a circle is square centimeters. a. Write an algebraic expression in terms of r that could be used to find the radius of the circle. b. Find the radius to the nearest tenth. a. b cm F 78.5 ft 2 G ft 2 H ft 2 J ft 2 H Find the circumference of each circle. Round to the nearest tenth. 41. radius: 8 in in. 42. radius: 12.5 ft 78.5 ft 43. diameter: 21 cm 66.0 cm esolutions Manual - Powered by Cognero Page 5
6 Find the area of each figure m cm in Find the product of and. Find each sum esolutions Manual - Powered by Cognero Page 6
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