Topics
8. Circles
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United States of AmericaVirginia
Grade 6

8.03 Area of a circle

Lesson
Practice

Area of a circle

We already know that area is the space inside a 2D shape. We can find the area of a circle, but we will need a special rule.

Let's look at what happens when we unravel segments of a circle.

Exploration

Slide the first slider to unravel the circle. Once unraveled, slide the second slider to piece the triangles together.

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  1. Explain how the width of the shape relates to the circumference of the circle.
  2. What figure is formed? Explain how the area of this figure relates to the area of the circle.

We can calculate the area of a circle using the formula:

\displaystyle A = \pi r^{2}
\bm{A}
Area of the circle
\bm{r}
Radius of the circle

Examples

Example 1

Find the area of the circle shown, correct to one decimal place.

A circle with a radius of 6 centimeters.
Worked Solution
Create a strategy

The area of a circle can be found using the formula: A=\pi r^{2}.

Apply the idea
\displaystyle A\displaystyle =\displaystyle \pi \cdot (6)^{2}Substitute r=6
\displaystyle =\displaystyle 113.1 \operatorname{ cm}^{2}Evaluate

Example 2

If the diameter of the circle is 24 \operatorname{ cm} , find its area correct to one decimal place.

Worked Solution
Create a strategy

Remember that the radius of a circle is half its diameter, r=\dfrac{d}{2}.

Apply the idea
\displaystyle r\displaystyle =\displaystyle \dfrac{24}{2}Divide the diameter by 2
\displaystyle =\displaystyle 12Evaluate
\displaystyle A\displaystyle =\displaystyle \pi \cdot 12^{2}Substitute r
\displaystyle =\displaystyle 452.4\operatorname{ cm}^{2}Evaluate

Example 3

Carlo and his friends ordered a pizza on a Saturday night. Each slice was 10\operatorname{ cm} in length.

Find the area of the pizza that Carlo and his friends ordered. Use 3.14 to approximate \pi.

Worked Solution
Create a strategy

The length of the pizza is the radius of the pizza. Use the formula of the area of the circle to find the area of the pizza.

Apply the idea
\displaystyle A\displaystyle =\displaystyle 3.14(10)^{2}Substitute the value of the \pi and the radius
\displaystyle =\displaystyle 314Evaluate

The area of the pizza is 314\operatorname{ cm}^{2}.

Idea summary
\displaystyle \text{Area of a circle}=\pi r^2
\bm{r}
Radius of the circle

Outcomes

6.MG.1

The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.

6.MG.1e

Solve problems, including those in context, involving circumference and area of a circle when given the length of the diameter or radius.

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