# Relating Area to Circumference

Warmup

A circular field is set into a square with sides 800 m.

Activity #1

Relate 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.

• Click “Show Circumference” to see if it reminds you of what the circumference of a circle is.
• Also click “Show Area” to see if that reminds you of what the area of a circle is.
• Then, answer the questions below.

(1.) What is formula for finding the circumference of a circle?

(2.) What is the circumference of the circle above?

(3.) What is the formula for finding the area of a circle?

(4.) What is the area of the circle above?

• Use the radius slider to do more examples as you can.

Activity #2

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.

(1.) How do the areas of the two shapes compare?

(2.) What polygon does the shape made of the circle pieces resemble?

(3.) How could you find the area of this polygon?

Activity #3

Application of Area.

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

• Watch the animation below and answer the questions that follow.

(1.) What polygon does the new shape resemble?

(2.) How does the area of the polygon in the applet compare to the area of the circle?

(3.) How can you find the area of the polygon?

(4.) State, in detailed steps, how you could find the polygon’s area in terms of the circle’s measurements. Show your thinking.

Challenge #1

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?

Challenge #2

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.

Challenge #3

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

Quiz Time