Seventh Grade Geometry Unit 5

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Seventh GradeGeometry Unit 5
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Warm Up

• 1) Complementary angles add up to ______.
• 2) The angles in a triangle add up to _______.
• 3) _________________________ is when you find the
  average distance from the mean of a set of data.
• 4) -2n -8 6n -9
• 5) The formula for the area of a triangle is
  ______.

90º
180º
Mean absolute deviation
4n - 17
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Warm Up

1. The seventh grade class is building a mini-golf
   game for the school carnival. The end of the
   putting green will be a circle. If the circle is
   10 feet in diameter, how many square feet of
   grass carpet will they need to buy to cover the
   circle?
2. 12y - 5 - n -7y - 3 8n

A ?r² A 3.14 (5)² A 78.5 ft²
7n 5y -8
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2a 8 units
2a 4 units²
3) Evaluate the perimeter and area if a 2.
Perimeter is 12 units Area is 8 units²
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Homework Check
Area 7.065 cm²
Radius is approx. 7
C 50.24 cm
Diameter is 10
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Standard

• CC.7.G.4. Know the formulas for the area and
  circumference of a circle and use them to solve
  problems give an informal derivation of the
  relationship between the circumference and area
  of a circle.

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Essential Questions

• How are the diameter and circumference of a
  circle related?
• What is pi? How does it relate to the
  circumference and diameter of a circle?
• How do we find the circumference of a circle?
• How do the areas of squares relate to the area of
  circles?

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Vocabulary

• Circumference the distance around a circle.
• Diameter the distance across a circle making
  certain to go through the center.
• Radius the distance from any point on a circle
  to the center.

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How are the diameter and circumference of a
circle related?
It takes 3.14 diameters of any circle to be
equivalent to its circumference. This is pi.
Circumference p?d
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How does the area of a circle relate to the area
of a rectangle?
http//www.rkm.com.au/ANIMATIONS/animation-Circle-
Area-Derivation.html
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How are the areas of a circle and triangle
related?
http//curvebank.calstatela.edu/circle2/circle2.ht
m
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Circle Formulas

• C p?d
• A p?r²

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Find the circumference and area of the circles
below.
9 cm
What is the scale factor of the radii?
_______ What is the scale factor of the
circumferences?____ What is the scale factor of
the areas? _______
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C p?d C 3.14 ? 6 C 18.84 cm A p?r² A
3.14 ? 9 A 28.26 cm²
C p?d C 3.14 ? 18 C 56.52 cm A p?r² A
3.14 ? 81 A 254.34 cm²
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9
14
Find the circumference and area of the circle
with a radius of 12.
12 cm
What is the scale factor of the radii?
_______ What is the scale factor of the
circumferences?____ What is the scale factor of
the areas? _______
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C p?d C 3.14 ? 24 C 75.36 cm A p?r² A
3.14 ? 144 A 452.16 cm²
C p?d C 3.14 ? 6 C 18.84 cm A p?r² A
3.14 ? 9 A 28.26 cm²
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16
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Find the circumference and area of the circles
below.
32 cm
8 cm
What is the scale factor of the diameters?
_______ What is the scale factor of the
circumferences?___ What is the scale factor of
the areas? _______
4
C p?d C 3.14 ? 32 C 100.48 cm A p?r² A
3.14 ? 256 A 803.84 cm²
C p?d C 3.14 ? 8 C 25.12cm A p?r² A
3.14 ? 16 A 50.24 cm²
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16
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3 in
3 in
3 in
Using the red and blue regions of the circle
above, how does the circumference and area change
when the radius is doubled? Circumference
doubles, but the area quadruples.
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• If a circle has a circumference of 29 p inches,
  what is the radius of that circle?

C p?d C 29p That means the diameter is 29
in. Therefore, the radius is 14.5 in.
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• Given that a circle has a circumference of 54
  feet, what is the APPROXIMATE area? (When asked
  to find approximate area, round EVERYTHING to the
  nearest whole number.)

A p?r² A 3 ? 81 A 243 ft²
C p?d 54ft 3 ? d 18 ft d
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• Mary wants to cover the top of a circular pillow
  with fur. The pillow has a radius of 8.5 inches.
  What amount of fur will she need to buy?

A p?r² A 3.14 ? 8.5² A 226.865 in²
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• Cam has a bike with 24 inch wheels (diameter).
  When he rides from his house to the store, his
  bike tires complete 50 revolutions. What is the
  distance IN FEET that he has traveled?

C p?d C 3.14 ? 24 in C 75.36 in This is only
one revolutionHe completed 50 revolutions
75.36 inches ? 50 3768 inches Dont forget to
convert inches to feet. 3768 12 314 feet.

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Find the area of the outermost region in the
circle below.
A p?r² A 3.14 ? 81 A 254.34 in²
3 in
3 in
3 in
A p?r² A 3.14 ? 36 A 113.04 in²
254.34 in² 113.04 in² 141.3 in²
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Pizza Crust
28.26
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(No Transcript)
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a 36
C 3.14 ? 2(3.39) C 21.2892
inches Approximately 21 inches
11.46
r 11.46
r 3.39 inches
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• If a circle is cut from a square piece of
  plywood, how much plywood would be left over?

The area of the square is 28 x 28 or 784 in². The
diameter of the circle is equal to the length of
the side of the square, or 28, so the radius
would be 14. The area of the circle would be
approximately 615.44 in². The difference in the
amounts (plywood left over) would be 168.56 in²
(784 615.44).
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What is the perimeter of the inside of the track?
The ends of the track are two semicircles,
which would form one circle with a diameter of
62m. The circumference of this part would be
194.68 m. Add this to the two lengths of the
rectangle and the perimeter is 2194.68 m
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Closing

• What is circumference and how do you find
  circumference of a circle?
• What is area and how do you find the area of a
  circle?

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Closing

• How are circumference and diameter related?
• How are the scale factors of circumference and
  area related?

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Homework
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Homework
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Area, Perimeter, and Circumference Jeopardy