Practice 6.5.1: Circumference and Area of a Gircle

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Practice 6.5.1: Circumference and Area of a Gircle UillT 6 . ffi$ffi*1ffi$ WfiTIE &rum ffi{!T${0t}T ffiffiffiffimilr,$ATffi$ Lesson 5: Ephining and Applyrng Area and Volume Fonnulas Practice 6.5.1: Circumference and Area of a Gircle Use your knowledge ofcircumference and area to complete each problem. 1. A circle has a regular octagon inscribed in ir The circle has a radius of4 meters. Find the perimeter of the octagoo. Use the formula Znrto find the circumference ofthe circle. Why is thq circumference found by using the formula a different length than the perimeter of the octagon? 2. A circle has a regular dodecagon (U-sided polygon) inscribed in it. The circle has a radius of 4 meters. Find the perimeter ofthe dodecagon. Then, find &e circrmrference ofthe circle using 2zrr. Why is the circumference found by'rsing the formula a different luogth than the perimeter ofthe dodecagon? 3. Cornpare the results ofproblerrs l and 2. Which dissection is a better ofthe circumference of the circle? Use a l}sided regular polygon as the inscribed figure in a circle that has a radius of4 meten Calculate the potygon's perimeter and compare it with the circle's circurnference- A circle has a regular octagon inscribed in it. The circle has a radius of 4 meters. Find the area of the circle using the formula.A = rEtz,then find the area of the octagon. Why ir the area ofthe circle different from the area ofthe octagon? 5. A circle has a regular dodecagon inscribed in it. The circle has a radius of4 meters. Find the area of the circle and then of the dodecagon. Why is the area ofthe circle dtfferent from the area ofthe dodecagon? UillT 6 o ffiilffiffiLHS k'tflTH &ffiffi W[TFf,ffiffiT #ffiSffim[N,&TfiS Lesson 5: Erylaining and Applying Area and Volume Formulas 6. Compare the results ofproblems 4 and 5. Which dissection is a better approximation ofthe area of the circle? Use a 3&sided regular polygon as the inscribed figur. in a circle that has a radius of 4 meters. Calculate the polygont area and compare it with the circle's area. 7. A round dining room table has a wood top with a circumference of 32 feet. A woodworker is refinishing th. top. He needs to find the area of the top to bny materials and know how long the job will take. What is the area of the tabletop? 8. Apiuahas a circurrference of40 inches. What is the area ofthe pina? 9. A carpenter is installing cuned wood nim around a circular window. The window is a circle that has an area of 50 square feet. How many feet ofwood trim are needed to surround the window? Measure the trim based on the length of the wood next to the window. 10. An artist paints a large blue circle on a yellow wal[. The area of the painted circle is 150 square feet. What is the circumference of the circle?.
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