Lesson 9
Applying Area of Circles
Problem 1
A circle with a 12-inch diameter is folded in half and then folded in half again. What is the area of the resulting shape?
Solution
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Problem 2
Find the area of the shaded region. Express your answer in terms of \(\pi\).
![A shaded rectangle with three unshaded circles stacked one above the other inside the rectangle.](https://cms-im.s3.amazonaws.com/uXfzZqm4L4sfs1Nuy2koUcs3?response-content-disposition=inline%3B%20filename%3D%227-7.3.B.PP.Image.12.png%22%3B%20filename%2A%3DUTF-8%27%277-7.3.B.PP.Image.12.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4a5f5e1281c07ed98c81989feddfdb9c4af5ffa99d6c19f7b4134d4d1287bcbf)
Solution
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Problem 3
The face of a clock has a circumference of 63 in. What is the area of the face of the clock?
Solution
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(From Unit 3, Lesson 8.)Problem 4
Which of these pairs of quantities are proportional to each other? For the quantities that are proportional, what is the constant of proportionality?
- Radius and diameter of a circle
- Radius and circumference of a circle
- Radius and area of a circle
- Diameter and circumference of a circle
- Diameter and area of a circle
Solution
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(From Unit 3, Lesson 7.)Problem 5
Find the area of this shape in two different ways.
![An odd 6-sided shape with some sides labeled. Starting at the top and moving clockwise, 1 m, 4 m, 3 m, unknown, unknown, 2 m.](https://cms-im.s3.amazonaws.com/Ast4GK7McsH9K1p44XPaboXV?response-content-disposition=inline%3B%20filename%3D%227.3.PP.New.Image.13.png%22%3B%20filename%2A%3DUTF-8%27%277.3.PP.New.Image.13.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fc057654645d845835a4a9cb9a018ee6e2f9799af03a09e814204b4cf5d4dfb6)
Solution
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(From Unit 3, Lesson 6.)Problem 6
Elena and Jada both read at a constant rate, but Elena reads more slowly. For every 4 pages that Elena can read, Jada can read 5.
- Complete the table.
pages read by Elena pages read by Jada 4 5 1 9 \(e\) 15 \(j\) - Here is an equation for the table: \(j = 1.25e\). What does the 1.25 mean?
- Write an equation for this relationship that starts \(e = \text{...}\)
Solution
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(From Unit 2, Lesson 5.)