Lesson 9
Applying Area of Circles
Let’s find the areas of shapes made up 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?
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T133902Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=53d5be7aef808c71ec6d3a7e26c8d976eb2a261bcf1a1f7b9c3634ba110ce236)
Problem 3
The face of a clock has a circumference of 63 in. What is the area of the face of the clock?
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
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T133902Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b52c4b97bdaad401f45c902fd455b9ca6a6cdba0f5de60c142618d610489d9a2)
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 \(e = \text{...}\)