# Distinguishing Circumference and Area

Warmup

Activity #1

Sort Out Area and Circumference (Exercise).

Solve the following problems to demonstrate your understanding of the difference between area and circumference of a circle. • Sort the cards into two groups based on whether you would use the circumference or the area of the circle to answer the question.

Activity #2

Find Area and Circumference (Exercise).

A goat (point G) is tied with a 6-foot rope to the corner of a shed. The floor of the shed is a square whose sides are each 3 feet long. The shed is closed and the goat can’t go inside. The space all around the shed is flat, grassy, and the goat can’t reach any other structures or objects. • Study the diagram carefully and answer the question below.

What is the area over which the goat can roam?

• Use the applet below to find the area and circumference of a circle.
• Click “New” to generate another circle and find its are and circumference.
• Do as many as time allows you.

Activity #3

Find Circumference and Area (Exercise).

The city of Paris, France is completely contained within an almost circular road that goes around the edge. • Use the map above with its scale to:​

(1.) Estimate the circumference of Paris.

(2.) Estimate the area of Paris.

• For each problem below, decide whether the circumference of the circle or the area of the circle is most useful for finding a solution. Explain your reasoning.

(1.) A car’s wheels spin at 1000 revolutions per minute. The diameter of the wheels is 23 inches. You want to know how fast the car is travelling.

(2.) A circular kitchen table has a diameter of 60 inches. You want to know how much fabric is needed to cover the table top.

(3.) A circular puzzle is 20 inches in diameter. All of the pieces are about the same size. You want to know about how many pieces there are in the puzzle.

(4.) You want to know about how long it takes to walk around a circular pond.

Challenge #1

Here below is a diagram of a softball field. Study it and answer the questions that follow.

(1.) About how long is the fence around the field?

(2.) About how big is the outfield?

Challenge #2

The floor of the shed is a square whose sides are each 3 feet long. The shed is closed and the goat can’t go inside. The space all around the shed is flat, grassy, and the goat can’t reach any other structures or objects.

What is the area over which the goat can roam?

Challenge #3

How many feet are traveled by a person riding once around the merry-go-round?

Here below are two students’ answers:

• Clare says, “The radius of the merry-go-round is about 4 feet, so the distance around the edge is about  8π  feet.”
• Andre says, “The diameter of the merry-go-round is about 4 feet, so the distance around the edge is about  4π  feet.”

(1.) Who do you agree with? 