Lesson 15
Area of a Circle
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=20240718T032222Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cffaadfe56f7c947a6e548c135566816770c57e85eeb2cad8a6dfc1faa2972c9)
Solution
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Problem 2
A circle’s circumference is approximately 76 cm. Estimate the radius, diameter, and area of the circle.
Solution
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Problem 3
Jada paints a circular table that has a diameter of 37 inches. What is the area of the table?
Solution
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Problem 4
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=20240718T032222Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4a063e3942a776f12f96edf4bc965787fcbf51321cabe9270333558c975dd37a)
Solution
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(From Unit 5, Lesson 12.)Problem 5
The Carousel on the National Mall has 4 rings of horses. Kiran is riding on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is.
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In one rotation of the carousel, how much farther does Mai travel than Kiran?
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One rotation of the carousel takes 12 seconds. How much faster does Mai travel than Kiran?
Solution
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(From Unit 5, Lesson 13.)