Seventh GradeGeometry

Unit 5

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 -95) The formula for the area of a triangle is ______.

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

Warm Up

3) Evaluate the perimeter and area if a = 2.

Homework Check

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 = πd

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

How are the areas of a circle and triangle related?

http://curvebank.calstatela.edu/circle2/circle2.htm

Circle Formulas

C = πdA = πr²

Find the circumference and area of the circles below.

C = πdC = 3.14 6C = 18.84 cm

A = πr²A = 3.14 9A = 28.26 cm²

9 cm

C = πdC = 3.14 18C = 56.52 cm

A = πr²A = 3.14 81A = 254.34 cm²

What is the scale factor of the radii? _______

What is the scale factor of the circumferences?____

What is the scale factor of the areas? _______

Find the circumference and area of the circle with a radius of 12.

12 cm

C = πdC = 3.14 24C = 75.36 cm

A = πr²A = 3.14 144A = 452.16 cm²

C = πdC = 3.14 6C = 18.84 cm

A = πr²A = 3.14 9A = 28.26 cm²

What is the scale factor of the radii? _______

What is the scale factor of the circumferences?____

What is the scale factor of the areas? _______

Find the circumference and area of the circles below.

32 cm

C = πdC = 3.14 32C = 100.48 cm

A = πr²A = 3.14 256A = 803.84 cm²

8 cm

C = πdC = 3.14 8C = 25.12cm

A = πr²A = 3.14 16A = 50.24 cm²

What is the scale factor of the diameters? _______

What is the scale factor of the circumferences?___

What is the scale factor of the areas? _______

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?

If a circle has a circumference of 29 π inches, what is the radius of that circle?

C = πdC = 29πThat means the diameter is __ in.Therefore, the radius is ___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 = πd

A = πr²

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 = πr²A =

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 = πd

3 in

3 in

3 in

Find the area of the outermost region in the circle below.

A = πr²

Pizza Crust

28”

If a circle is cut from a square piece of plywood, how much plywood would be left over?

What is the perimeter of the inside of the track?

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