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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143511Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f7c7324bc21f88ae71c166f4f5147294d21d8ed33121fc38a602824098f69762)
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143511Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8046cda5834203f1e3d814a719e83c1cdb3e9613b197d8d507da369e4a40590e)