Transcript Seventh Grade Geometry Unit 5

Seventh Grade
Geometry
Unit 5
Warm Up
90º
1) Complementary angles add up to ______.
180º
2) The angles in a triangle add up to _______.
Mean absolute deviation
3) _________________________
is when you find
the average distance from the mean of a set of
data.
4n - 17
4) -2n -8 + 6n -9
5) The formula for the area of a triangle is ______.
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
A = Πr²
the circle?
A = 3.14 (5)²
A = 78.5 ft²
2) 12y - 5 - n -7y - 3 + 8n
7n + 5y -8
2a + 8 units
2a + 4 units²
3) Evaluate the perimeter and area if a = 2.
Perimeter is 12 units
Area is 8 units²
Homework Check
Area = 7.065 cm²
Radius is approx. 7
C = 50.24 cm
Diameter is 10
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.
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?
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.
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 = πd
How does the area of a circle relate to
the area of a rectangle?
http://www.rkm.com.au/ANIMATIONS/animati
on-Circle-Area-Derivation.html
How are the areas of a circle and
triangle related?
http://curvebank.calstatela.edu/circle2/circle2.htm
Circle Formulas
C = πd
A = πr²
Find the circumference and
area of the circles below.
9 cm
What is the scale
factor of the radii?
_______
3
C = πd
C = 3.14  6
C = 18.84 cm
C = πd
C = 3.14  18
C = 56.52 cm
A = πr²
A = 3.14  9
A = 28.26 cm²
A = πr²
A = 3.14  81
A = 254.34 cm²
What is the scale
factor of the
3
circumferences?____
What is the scale
factor of the areas?
9
_______
Find the circumference and area
of the circle with a radius of 12.
12 cm
What is the scale
factor of the radii?
4_______
C = πd
C = 3.14  6
C = 18.84 cm
A = πr²
A = 3.14  9
A = 28.26 cm²
C = πd
C = 3.14  24
C = 75.36 cm
A = πr²
A = 3.14  144
A = 452.16 cm²
What is the scale
factor of the
4
circumferences?____
What is the scale
factor of the areas?
16
_______
Find the circumference and
area of the circles below.
8 cm
32 cm
What is the scale
factor of the
diameters?
4
_______
C = πd
C = 3.14  8
C = 25.12cm
C = πd
C = 3.14  32
C = 100.48 cm
What is the scale
factor of the
4
circumferences?___
A = πr²
A = 3.14  16
A = 50.24 cm²
A = πr²
A = 3.14  256
A = 803.84 cm²
What is the scale
factor of the areas?
16
_______
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.
If a circle has a circumference of 29 π inches,
what is the radius of that circle?
C = πd
C = 29π
That means the diameter is 29 in.
Therefore, the radius is 14.5 in.
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.)
C = πd
54ft = 3  d
18 ft = d
A = πr²
A = 3  81
A = 243 ft²
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 = πr²
A = 3.14  8.5²
A = 226.865 in²
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 = πd
C= 3.14  24 in
C= 75.36 in
This is only one revolution…He completed 50 revolutions…
75.36 inches  50 = 3768 inches
Don’t forget to convert inches to feet.
3768 ÷ 12 = 314 feet.
Find the area of the outermost region in the circle below.
3 in
A = πr²
A = 3.14  81
A = 254.34 in²
A = πr²
A = 3.14  36
A = 113.04 in²
254.34 in² – 113.04 in² = 141.3 in²
Pizza Crust
28.26
a = 36
= 11.46
r = 11.46
r = 3.39 inches
C = 3.14  2(3.39)
C = 21.2892 inches
Approximately 21 inches
If a circle is cut from a square piece of
plywood, how much plywood would be left
over?
28”
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).
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
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?
Closing
How are circumference and diameter related?
How are the scale factors of circumference and
area related?
Homework
Homework
Area, Perimeter, and Circumference
Jeopardy