day 7 area of a circle
TRANSCRIPT
Area of Circles.notebook
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Do NowAIM: Area of a Circle
-3(x + 5) = -30
Solve the following equation and check your answer.
CHECK
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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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1 Explore: Finding the Area of a circle
b
h
The base and height of the parallelogram relate to the parts of the circle.
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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1 Explore: Finding the Area of a circle
b
h
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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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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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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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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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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Reflect
Does the formula work for a circle with a radius of 3 inches? Show your work below.
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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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Homework
On Core Page 118 #1-12 all