MEA 502 LESSON _NOTES Period____________ CRS SKILL MEA 502 Name_________________________________________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION MEA 402 Use geometric formulas when all necessary information is given Level 2 – MOST students will MEA 502 Compute the area and circumference of attain mastery of the focus skill in circles after identifying necessary information isolation. Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will MEA 601 Use relationships involving area, perimeter, attain mastery of the extension and volume or geometric figures to compute another skill. measure VOCABULARY Radius, Diameter, Circumference, Cylinder, Sphere, REQUIRED SKILL TO MASTER Radius, diameter and circumference; Area of a circle •
Activity One Circumference of a Circle Trace a circular object that fits in the space below. Measure the diameter (D) and circumference (C) of the circle to the nearest tenth of a centimeter. Label these measures on your drawing. Also indicate a radius (C) on your drawing. •
Calculate the ratio of C:D. This ratio should be close to 3.14. If it is not please measure again or ask for assistance. •
Since C
= π we can use algebra to find C=π D or C=2π R D
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Activity two Area of a circle Fold a paper plate in half four times to divide it into 16 equal-­‐
sized sections. Label the radius r as shown. Let C represent the circumference of the circle. Cut out each section; reassemble to form a parallelogram-­‐
shaped figure. 1. What is the measurement of the base and height? 2. Substitute these values into the formula for the area of a parallelogram. 3. Replace C with the expression for the circumference of a circle, 2πr. Simplify the equation and describe what it represents. Circumference and Area of a circle C= circumference R=radius D=diameter A=area C = π D = 2π R A = π R 2 2 Level 1 1. The radius of the face of a clock is 5 inches. Find the circumference of the face of the clock. Round your answer to the nearest whole number. 2. Find the area of the face of the same clock with a radius of 5 inches. Round your answer to the nearest whole number. 3. What is the Perimeter and Area of the circle below to nearest thousandth of an inch? Level 2 4. A circular sidewalk surrounds a circular pool. The circular sidewalk is 3 feet wide. The diameter of the sidewalk and pool is 26 feet. a. What is the diameter of the pool? b. What is the area of the sidewalk? c. What is the area of the pool? d. What is the circumference of the pool? e. What is the circumference of the outside circle of the sidewalk? 3 5. Tory is going to be in a dart tournament. The dartboard
in the tournament looks like the one pictured
below. When Tory throws a dart, the dart will have a
better chance landing in the part of the dartboard with
the larger area. Which area will Tory's dart most likely
land in, the gray area or the white area? Show your
work. Level 3 6. An air traffic control radar screen is a circle with a diameter of 24 inches. a. What is the area of the screen to the nearest square inch? b. The radar screen is set to have a scale of 6 inches:25 nautical miles. To the nearest square nautical mile, what is the area of the circular region covered by the radar? 7. The radius of a circular racetrack is 234 feet. How many times must a car go around the track to travel 10 miles? 4 8. The rim of the bicycle wheel shown has a radius of 13 inches. What is the circumference of the rim of the wheel to the nearest 10th of an inch? 9. The rim of the bicycle wheel below has a diameter of 24 inches. When the tire is mounted on the wheel, the diameter of the wheel increases as shown. To the nearest tenth of an inch, how much does the circumference of the bicycle wheel increase after the tire is mounted? 10. The bicycle wheel shown below has a diameter of 2 feet. To the nearest whole number, how many revolutions will the wheel make when it rolls one mile? 11. Suppose that cleaning up an oil slick from the surface of a lake costs $200,000 if the oil slick is circular in shape with a radius of 2 miles. Assuming that the cost of cleaning up the oil slick depends upon its size (area), what would be the cost of cleaning up a circular oil slick with a radius of 1/2 mile? 5 12. What is the circumference of a circle with a radius of 5/16 yard? Level 4 13. Hugo ordered two circular pizzas, each with a diameter of 10 inches. Greg ordered one circular pizza with an area equal to the sum of the areas of Hugo’s two pizzas. What was the diameter of Greg’s pizza? 14. A landscape architect used the entire length of an 80-­‐foot rope to lay out a flower bed in the shape of a square. In another area, he used the entire length of the same rope to lay out a second flower bed in the shape of a circle. How many square feet greater is the area of one flower bed than the other? (Drawings are not to scale.) 15. A racer’s bicycle wheel has a diameter of 2 feet 4 inches and makes 360 revolutions per minute. To the nearest tenth of a mile, how far will the bicycle travel in 5 minutes? 6 Level 5 (Please see math reference sheet for many formulas needed in this class.) 16. Find the volume and surface area of each of the following cylinders. a. b. 17. A soft drink can has a diameter of 6 cm and a height of 11.5 cm. a. What is its volume? b. What is its surface area? 18. A lawn roller is 1 m wide and 80 cm high. What area is covered in each revolution? 19. The height of a cylinder is 30 cm. Find the surface area of the cylinder if its volume is 750π cm3. 7 20. Quinn collects sap in a cylindrical bucket having a diameter of 10 inches. If the bucket is filled with maple sap to a depth of 5 inches, how many gallons of sap does it contain? Give your answer to the nearest tenth of a gallon. (Use 1 gallon= 231 cubic inches.) 21. Find the volume and surface area of each cone below. a. b. 22. Find the volume and surface area of the spheres below. a. b. 8 23. About 70% of earth is covered in water, making 30% of earth potentially habitable by humans. Earth can be modeled as a sphere with diameter 12,700 km. There are 7.1 billion people in the world. What is the population density of potentially habitable earth? 24. One ice chest is shaped like a rectangular prism with the exterior dimensions shown below. A second ice chest is shaped like a cylinder with the exterior dimensions shown. The bottom, sides, and top of both ice chests are made of plastic that is 2 inches thick. Which of the two chest would hold the most ice? 9