Lesson 7
Exploring the Area of a Circle
Let’s investigate the areas of circles.
Problem 1
The \(x\)-axis of each graph has the diameter of a circle in meters. Label the \(y\)-axis on each graph with the appropriate measurement of a circle:
radius (m), circumference (m), or area (m2).
![Three graphs. Horizontal axis, diameter in meters, scale 0 to 10, by 2's. Vertical axis, scale 0 to 20, by 2's.](https://cms-im.s3.amazonaws.com/7tLTaGajXMahJheC9pkoCPkp?response-content-disposition=inline%3B%20filename%3D%227-7.3.B.PP.Image.14.png%22%3B%20filename%2A%3DUTF-8%27%277-7.3.B.PP.Image.14.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T010856Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=86f707da3bed5ed4b61d5b34e8ef3ca951b6ef5b346cb95577f1846e2d35b5de)
Problem 2
Circle A has area 500 in2. The diameter of circle B is three times the diameter of circle A. Estimate the area of circle B.
Problem 3
Lin’s bike travels 100 meters when her wheels rotate 55 times. What is the circumference of her wheels?
Problem 4
Priya drew a circle whose circumference is 25 cm. Clare drew a circle whose diameter is 3 times the diameter of Priya’s circle. What is the circumference of Clare’s circle?
Problem 5
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Here is a picture of two squares and a circle. Use the picture to explain why the area of this circle is more than 2 square units but less than 4 square units.
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Here is another picture of two squares and a circle. Use the picture to explain why the area of this circle is more than 18 square units and less than 36 square units.
Problem 6
Point \(A\) is the center of the circle, and the length of \(CD\) is 15 centimeters. Find the circumference of this circle.
![A circle with center point A. Diameter CD, 15 cm. Points on the circle are C, E, G, B, D.](https://cms-im.s3.amazonaws.com/XZFdo8Xegbwd8idriKFxdh2F?response-content-disposition=inline%3B%20filename%3D%227.3.PP.New.Image.10.png%22%3B%20filename%2A%3DUTF-8%27%277.3.PP.New.Image.10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T010856Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2d970fd7626705f5949efad87f5f77a4cdf5f2619130274a8fb621c1f9e2cf09)