The document is about finding the area of circles. It explores rearranging a circle into a parallelogram shape to relate the circumference and radius to the base and height of the parallelogram. This leads to the formula for the area of a circle being πr^2. Examples are given of calculating the area when given the radius or diameter. It also explores the relationship between the circumference and area, deriving the formula A=C^2/4π.

1. Area of Circles.notebook April 16, 2013
AIM: Area of a Circle
Do Now
Solve the following equation and check
your answer.
-3(x + 5) = -30 CHECK
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2. Area of Circles.notebook April 16, 2013
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3. Area of Circles.notebook April 16, 2013
1 Explore: Finding the Area of a circle
You can use what you know about circles and pi to
help find the formula of the area of a circle.
We can rearrange the parts of the circle
to form a parallelogram.
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4. Area of Circles.notebook April 16, 2013
1 Explore: Finding the Area of a circle
The base and height of the parallelogram
relate to the parts of the circle.
h
b
base b = the circumference of the circle or _____.
height h =the______ of the circle or _____.
To find the area of a parallelogram, the equation is A = ____
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5. Area of Circles.notebook April 16, 2013
1 Explore: Finding the Area of a circle
h
b
To find the area of the circle, substitute for b and h in the
area formula.
1a. Conjecture: Make a conjecture about the
lengths of all the radii of a circle.
1b. How can you make the wedges look more like a
parallelogram?
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6. Area of Circles.notebook April 16, 2013
AREA OF A CIRCLE
The area of a circle is equal to π times the radius
squared.
2 EXAMPLE - Finding the Area of a Circle
A biscuit recipe calls for the dough to be rolled out and
circles to be cut from the dough. Find the area of the
biscuit once it is cut. Use the pi button.
4cm
The area of the biscuit is about _______.
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7. Area of Circles.notebook April 16, 2013
Try This!
2a. A flower garden is in the shape of a circle with a
diameter of 10yds. What is the area of the garden? Use the
pi button.
The area of the garden is about __________.
2b. A circular pool has a radius of 10ft. What is the area of
the pool? Use the pi button.
The area of the pool is about __________.
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8. Area of Circles.notebook April 16, 2013
Reflect
2c. Compare finding the area of a circle when given the
radius with finding the area when given the diameter.
2d. How could you estimate or check the reasonableness
of an answer for the area of a circle?
2e. Why do you evaluate the power in the equation
before multiplying
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9. Area of Circles.notebook April 16, 2013
3 Explore - Finding the relationship
between Circumference and Area
Start with a circle that has a radius r.
Solve the equation C = 2πr for r.
Substitute your expression for
r in the formula for area of a
circle.
Square the term in the parenthesis.
Evaluate the power.
Simplify.
Solve for C2.
The cirumference of the circle squared is equal to ___________.
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10. Area of Circles.notebook April 16, 2013
Reflect
Does the formula work for a circle with a radius of 3
inches? Show your work below.
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11. Area of Circles.notebook April 16, 2013
Try This!
=
Find the area of the circles given the circumference.
Give your answers in terms of π.
3b. C = 8π, A=____________
3c. C = π, A=____________
3d. C = 2π, A=____________
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12. Area of Circles.notebook April 16, 2013
Homework
On Core Page 118 #1-12 all
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