Relating Area to Circumference

A circular field is set into a square with an 800 m side length.

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Realate Area to Circumference of a Circle.

Hopefully, the names of the three buttons on the left give you an idea of what they each do, but go ahead and click the first two to see if they remind you of the difference between circumference and area. Then answer Questions #1 and #2 below. Change the value of the radius and practice more.

(1). What is circumference, and what is the formula for it?

(2). What is the area of a circle, and what is the formula for it?

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More on Exploring the Area of a Circle.

Here below are two circles of equal measure. The top circle is separated into fourths and the bottom circle is separated into eighths.

Use the points to move the pieces and use the open circles to rotate them. Arrange the parts in a row so that the curved edges are alternating between top and bottom.

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Application of Area.

Imagine a circle made of rings that can bend but not stretch.

Watch the animation below.

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A local pizzeria sells small, medium, and large pizzas. A small is 9 inches in diameter, a medium is 12 inches in diameter, and a large is 15 inches in diameter. Prices for the pizzas are $6.00 for a small, $9.00 for a medium, and $12.00 for a large.

Use the slider d to change the diameter of the pizza.

(1). What other measure is closely related to the area of the pizza?

(2). What other measure is most closely related to the circumference of the pizza?

(3). Which measurement – Radius, Diameter, Circumference, or Area— seems most closely related to the price?

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Use pi as 3.14 to find area and circumference. Enter the area and the circumference of the circle. Press “New” button to get a randomly generated circle.

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The picture shows a circle divided into 8 equal wedges which are rearranged.

The radius of the circle is r and its circumference is  How does the picture help to explain why the area of the circle is