IM 7.3.8 Practice: Relating Area to Circumference

The picture shows a circle divided into 8 equal wedges which are rearranged.[br][br][img]data:image/png;base64,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[/img][br][br]The radius of the circle is [math]r[/math] and its circumference is [math]2\pi r[/math]. How does the picture help to explain why the area of the circle is [math]\pi r^2[/math]?
A circle’s circumference is approximately 76 cm. Estimate the radius, diameter, and area of the circle.
Jada paints a circular table that has a diameter of 37 inches. What is the area of the table?
[size=150]The Carousel on the National Mall has 4 rings of horses. Kiran is riding on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is.[/size][br][br]In one rotation of the carousel, how much farther does Mai travel than Kiran?
One rotation of the carousel takes 12 seconds. How much faster does Mai travel than Kiran?
Here are the diameters of four coins:
A coin rolls a distance of 33 cm in 5 rotations. Which coin is it?
A quarter makes 8 rotations. How far did it roll?
A dime rolls 41.8 cm. How many rotations did it make?[br]
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Information: IM 7.3.8 Practice: Relating Area to Circumference