MEA 502 Work Sheet Period Name. CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 402 Use geometric formulas when all necessary
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1 MEA 502 Work Sheet Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 402 Use geometric formulas when all necessary attain mastery at this level information is given MEA 502 Level 2 MOST students will attain mastery of the focus skill in 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 attain mastery of the extension skill. MEA 502 Compute the area and circumference of circles after identifying necessary information MEA 601 Use relationships involving area, perimeter, and volume or geometric figures to compute another measure Level 1 1. What is the circumference of a circle with the radius of feet to the nearest hundredth of a foot? 2. What is the area of the circle below? Leave your answer in terms of π ft. 3. A sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. To the nearest tenth, what is the maximum area of lawn that can we watered by the sprinkler? 1
2 Level 2 4. Kim is putting an 8- foot diameter circular flower garden in her yard. She will put plastic edging along the flowerbed. a. How many feet of edging will Kim need to enclose her flower garden? b. How many square feet of land are in Kim s garden? 5. Anna is covering her circular pool with a heavy- duty cover for the winter. The pool has a diameter of 24 feet. The cover extends 12 inches beyond the edge of the pool, and a rope runs along the edge of the cover to secure the cover in place. a. What is the area of the cover? Round your answer to the nearest square foot. b. What is the minimum length of the rope? Round your answer to the nearest foot. 6. A signal from a walkie- talkie can be received up to 1 mile away. A signal from a CB radio can be received up to 5 miles away. a. Over how great an area can a walkie- talkie transmit a signal? b. Over how great an area can a CB radio transmit a signal? c. Write a ratio to compare the area of a CB radio reception to the area of a walkie- talkie reception. 2
3 Level 3 7. The circular floor in the Pantheon in Rome has an area of about 1473 square meters. What is the diameter of the floor to the nearest tenth of a meter? 8. Trevor needs a new bicycle tire. His tire has a circumference of about inches. What is the diameter of his tire? Round your answer to the nearest inch. 9. A circular pizza that is 16 inches in diameter costs $ Assuming that the cost of such a pizza depends upon its size (area), what would be the cost of a pizza that is 8 inches in diameter? 10. Suppose that it takes 12 hours to decontaminate a circular chemical spill that has a radius of 6 feet. Assuming that the amount of time required to decontaminate such a spill depends upon its size (area), how many hours would it take to decontaminate a similar spill with a radius of 3 feet? 11. Grandma has an old family recipe for blueberry pancakes. She can make 8 pancakes that are each 10 inches in diameter. Grandma decided that the pancakes were way too large for her grandchildren and decided to make pancakes that were only 2 inches in diameter. How many small pancakes will Grandma s recipe make? 3
4 12. What is the area of the circle to the right? 13. What is the circumference of the circle to the right? 14. Below is a photo of a crop circle. What is the circumference of the crop circle to the nearest tenth of a foot? 15. What is the area of the crop circle to the nearest tenth of a square foot? 16. Your local pizza place offers the following two pizza deals, both for the same price: Option 1: One extra- large pizza 20 inches in diameter. Option 2: Two medium pizzas each 15 inches in diameter. Which option provides more pizza and therefore costs less per square inch? Express the areas in terms of π. (Type pi for π.) 17. A radio station sends a signal in a circular area with an 80- mile radius. Find the approximate area in square kilometers that receives the signal. 4
5 18. The True Blue Tablewear Company has an order for 12 tablecloths for a wedding. Each table is a circle with a diameter of 6 feet with 1- foot overhang. How many square feet of fabric will the True Blue Company needed to cover all the tables? Show your work. Round your answer to the nearest tenth of a square foot. 19. What is the circumference of a circle with a radius of 3 8 m? Level Ben draws a circle inside a square piece of paper whose area is 400 square inches. He makes sure than the circle touches each side of the square. What is the area of the circle? 21. In the diagram, the diameter of the large circle is 18 meters. All four small circles are the same size. Find the area of one small circle and the area of one large circle in terms of π. Then find the ratio of the area of a small circle to the area of the large circle. 5
6 22. Astronauts train for space flight in a centrifuge, which consist of a rotating arm with a cab at the outer end of the arm. The arm, which has a length of 58 feet, is revolved about the center of the centrifuge. An astronaut sits in the cab, which is then rotated 50 times per minute. To the nearest hundred feet, how far does the astronaut travel in one minute? 23. An engineer is tasked to install a pipe, which supplies water to a building. The new pipe must have a cross- sectional area of A=100π cm 2. What pipe diameter should the engineer choose? 24. If the area of a pizza is 144 in.², what is the length of the crust of the pizza in inches to the nearest tenth? 25. A half circle is drawn on each side of a right triangle as shown. What is the relationship among the areas of the 3 half circles? 26. Theo tied his dog, Flash, to a pole in the middle of the yard using a 10 ft. leash. Flash dug holes in the yard everywhere he could reach. Theo had to reseed the part of the lawn that Flash destroyed. Grass seed costs $1.40 per package and covers 50 square feet. What did it cost Theo to reseed the lawn? 6
7 Level Find the volume and surface area of the cylinders below. a. b. 28. Thelma and David built a recycling bin that is 6 feet wide, 12 feet long, and 14 feet high. How much trash can fit inside of the bin? 29. The cylindrical canister of a fire extinguisher has a radius of 4 inches and is 12 inches high. How many cubic inches can it hold? 7
8 30. A cylindrical glass that has a diameter of 8 cm and a height of 15 cm is full of water. The water is poured into a rectangular pan that measures 15 cm by 10 cm by 5 cm. Will the pan overflow? If so, by how much? If not, how much space is left in the pan? 31. A section of concrete pipe 30 m long has an inside diameter of 1.2 m and an outside diameter of 1.8 m. What is the volume of concrete in this section of pipe? 32. A rectangular strip of aluminum, 30 cm long and 10 cm wide, is rolled into the form of a cylinder. Which would have the greater volume, a cylinder 10 cm high with circumference of 30 cm or a cylinder 30 cm high with circumference of 10 cm? 33. Vermont cheddar cheese can be purchased in right circular cylinders called cheese wheels that are 9.5 inches in diameter and 5 inches tall that sell for $ New York sharp cheddar cheese also can be purchased as cylindrical cheese wheels that are 6 inches in diameter and 8 inches tall that sell for $95. Which wheel, Vermont or New York, is the better buy in terms of dollars per cubic inch? 8
9 34. Find the volume and surface area of each cone below. a. b. 35. Cindy went to Maggie Moo s for an ice cream cone after school. The ice cream cone had a radius of 1 inch, a height of 2 ½ inches, and a slant length of 3 ½ inches, how much ice cream could the cone hold? Only count the ice cream in the cone. 36. Find the volume and surface area of the spheres below. a. b. 9
10 37. Estimate the volume of air in a beach ball that has a 12 inch diameter. Round your answer to the nearest whole number. 38. Use the information about the Earth and Moon in the photo. a. Find the surface area of the Earth. b. Find the surface area of the Earth s moon. c. Compare the surface area of the Earth and its moon. d. About 70% of the Earths surface is water. How many square miles of water are on Earth s surface? Mixed Review 1. (5x 3 + 6x 2 3x + 1) + (5x 4 4x 2 + 2x 5) a) 10x 7 + 2x 4 x2 4 b) 10x 3 + 2x 2 x 4 c) 5x 4 + 5x 3 + 2x2 x 4 d) 5x 4 + 5x3 2x 2 + x 4 2. (7x 3 6x 2 + 4x + 1) + (5x 3 6x 2 4x + 5) a) 12x 6 12x b) 12x 3 + 8x + 6 c) 12x 3 12x 2 + 8x + 6 d) 12x 3 12x
11 3. (7x 3 6x 2 + 4x + 1) (5x 3 6x 2 4x + 5) a) 2x 3 8x 4 b) 2x 3 + 8x 4 c) 2x 3 12x 2 + 8x + 6 d) 2x 3 12x (5x 4 6x 3 + x 7) ( 2x 4 + 3x 3 + 4x 2 + 7x 3) a) 7x 4 3x 3 + 4x 2 + 8x 10 b) 7x 4 9x 3 4x 2 6x 4 c) 2x 4 9x 3 4x 2 6x 10 d) 2x 4 3x 3 + 4x 2 6x (5x 6)(x + 2) a) 5x 2 12 b) 10x 2 12x c) 5x 2 4x 12 d) 5x 2 + 4x (3x 1)(3x 1) a) 9x 2 1 b) 9x 2 6x + 1 c) 9x 2 6x 1 d) 9x Use the diagram to determine the measure of the given angles. Line m is parallel to line n. A= B= C= D= 11
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