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 $$\pi$$.

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?

1. Radius and diameter of a circle
2. Radius and circumference of a circle
3. Radius and area of a circle
4. Diameter and circumference of a circle
5. 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.

Solution

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(From Unit 3, Lesson 6.)

Problem 6

1. Complete the table.
4 5
1
9
$$e$$
15
$$j$$
2. Here is an equation for the table: $$j = 1.25e$$. What does the 1.25 mean?
3. Write an equation for this relationship that starts $$e = \text{...}$$

Solution

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(From Unit 2, Lesson 5.)