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Area of Circles
Students use radius, diameter, circumference, and the circle-area formula to solve problems.
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Beginner
15–20 minutes
Volume & Area
Volume & Area
Page 3 of 8
Inside Cover
Area of Circles
At a Glance
Binder SectionVolume & Area
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How does the radius determine every important measurement of a circle?
Build Understanding
The area of a circle is A = pi r squared. Always identify the radius before substituting. If the diameter is given, divide it by two.
For semicircles and sectors, find the corresponding fraction of the full circle. For shaded regions, subtract the inner area from the outer area.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Use A = pi r squared.
- Convert diameter to radius first.
- Keep exact answers in terms of pi.
- Use fractions for semicircles and sectors.
- Use square units.
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Interactive Vocabulary
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Worked Examples
Example 1
Circle with r=6
1
C=2πr=12π≈37.7 units.
2
A=πr²=36π≈113.1 square units.
Example 2
Diameter 18
1
r=9.
2
A=81π square units.
Ask and explain
Common Questions
Do I square pi? No, square only the radius.
If diameter is 10, is r also 10? No, r=5.
How is area different from circumference? Area is inside; circumference is around.
Notice and correct
Common Misconceptions
Using diameter as radius
Divide diameter by 2 first.
Forgetting to square radius in area
Circumference is linear; area uses r².
Learn Through Video
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Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
A circle has diameter 10. Find circumference and area.
2
We Do
Guided Practice
r=6: A=36 pi square units.
d=14: A=49 pi.
Semicircle r=8: A=32 pi.
Quarter-circle r=10: A=25 pi.
Annulus radii 9 and 4: A=65 pi.
3
You Do
Independent Practice
A circle has diameter 10. Find circumference and area.
Create and solve a second example with different values.
4
Stretch Your Thinking
Challenge & Real-World Practice
A circular path surrounds a circular garden. Determine the path’s area from two radii and explain why subtracting areas works.
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IXL
Area of Circles
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Area and Circumference of Circles
Open resourceDeltaMath
DeltaMath: Area of Circles
Open resourceDeltaMath: Area of Sectors and Shaded Regions
Open resource
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- I can identify the important information.
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Question 1
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Question 2
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