lesson 6...2017/12/12 · examples: find the area of a circle with a radius of 15 inches in terms...
TRANSCRIPT
Match the formula with what it calculates.a. A = πr2 b. A = bh c. C = πd d. A = 1/2 bh
1. Area of a rectangle 2. Area of a triangle3. Circumference of a circle 4. Area of a circle
Find the area and perimeter of each figure.
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5 cm6 cm
6.5 cm 5 cm
18 cm
8 cm
https://www.youtube.com/watch?v=flL_W2IkkqAcircle song
Content Objective: • I can perform calculations involving circles and sectors.• I can recognize that diameter and circumference form a proportional relationship.
Language Objective: • I can read a story problem and determine which values related to circles are given and which need to be calculated. (Hint cube the problem!)
Lesson 6.1A
Assignment: 6.1A Due:__________ Quiz after 6.1D
7.3.1.1
7.3.1.1
PerimeterPerimeter: Distance around the outside of a figure.
Find the distance around the following figures.
Lesson 6.1APerimeter, Circumference, and Area
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8 in
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6.3 in
4 in
50 in
78.5 in
5 in
Rectangle Square Triangle Sector
1.) 2.) 3.) 4.)
P = _______ P = ________ P=________ P =________
Find the missing radius or diameter of each circle (hint radius is half of the diameter):
Circles
Circle: A circle is a set of points, all of which arethe same distance from a given point. That given point is the center of the circle.
Diameter A diameter is a line that passes through the center of the circle and has endpoints on the circle.
Radius: A radius is any line segment from the center of the circle to a point on the circle.
5.) r = 3 cm 6.) d = 33 ft 7.) d = 16 in
d = ________ r =________ r =_______
I can perform calculations involving circles and sectors. 7.3.1.1I can recognize that diameter and circumference form a proportional relationship 7.3.1.1
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4 in||
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8 in
Circumference: The distance around the outside of a circle.Pi, π: The ratio of the circumference of a circle to its
diameter. It is an irrational number (a decimal number that never ends and never repeats).
Use the π key on your calculator or
approximate it with π ≈ 3.14 or 22/7Circumference Formulas: The circumference of a circle can be found with either of the following formulas (the formulas are equal because the diameter is equal to twice the radius, d = 2r).
C = πd C = 2πr
Example: Find the circumference of a circle with a diameter of 15 inches.
Circumference = diameter πC ≈ 15(3.14)C ≈ 47.1 inches
Find the circumference of the following circles.
8.) r = 3 cm 9.) d = 33 ft 10.) d = 16 in
C ≈ ___________ C ≈ ___________ C ≈ ___________
*11.) What is the diameter of a circle with a circumference of 122.46 inches? (hint: backtrack)
AreaThe area is how many square units of measure fit inside a figure. A figure's base and height must be perpendicular(make a 90 degree angle). Look for the symbol to find the right angle.Area Formulas:
Rectangle Square Triangle A = l w A = s2 A = 1/2bh
12.) A =____________ 13.) A = ___________ 14.) A = _____________
(Count the squares in each figure, does it match with the area found using the formulas?)
Circumference
3 cm
Area of CirclesArea formula A = πr2 for a circle:
Since π is an irrational number (a never ending, never repeating decimal) you can approximate it by using your π key on your calculator or by using 3.14 or 22/7.
Sometimes answers involving π are given "in terms of π" which simply means ~ make all the calculations except for multiplying by an approximation of π, instead keep the π symbol as part of the answer.
Examples: Find the area of a circle with a radius of 15 inches in terms of π.Area = π radius radius
A = (15)(15)πA = 225π in2
Now find the estimated area using an approximation for π.A≈ (225)3.14 = 706.5 in2
a.) Find the area of the following circles in terms of π. b.) Then find the area using 3.14 for π.
27 m36 ft
15a.) A = _________ 16a.) A = _________ 17a.) A = __________
15b.) A = _________ 16b.) A = _________ 17b.) A = __________
18.) What is the area of a circle with a radius of 7 feet?
19.) What is the area of a circle with a diameter of 16 feet?
20.) What is the radius of a circle with an area of 28.26 sq. inches? (hint: backtrack)
21.) What is the radius of a circle with an area of 78.5 sq. inches?
Answer in terms of pi, because π is still in the answer.
Check out homework problems 13 & 17!
Remember to show all of your work!!!!!!!
http://illuminations.nctm.org/Activity.aspx?id=3547Let's go to this websiteand see if we can find a pattern involving circumference and diameters.
22.) Start on the Intro screen and select diameter. Change the diameter of the circle and observe how it changes the circumference. Watch the videos and write down your observations.
23.) Change to the investigation screen and select the ratio button. Set the circumference as the numerator, diameter as the denominator, and click ok. Then record the results with different diameters by clicking add to the table. Check the cross products. What do notice?
24.) Fill in the table.
25.) Describe what you think a diametercircumference graph would look like.
Click to Watch Video
Change diameter here.
Diameter (cm)
1 2 3 4 5 6
15
14
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12
11
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9
8
7
6 5
4
3
2
1
Circumference
Diameter ~ Circumference Graph
26.) Make the graph using your table.27.) What is the scale factor from the diameter to the circumference?
28.) What type of relationship do diameter and circumference have?
Here is a circle, it knows how to get around.It has a radius from center to rim.And it's diameter is a line that goes from side to side while passing through the center. Now isn't that simple.
r squared sounds like area to me.When I need a circumference I will just use d.