Seventh Grade Geometry 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 n -9 5) 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 n -7y n 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 = π  d

How does the area of a circle relate to the area of a rectangle? on-Circle-Area-Derivation.html

How are the areas of a circle and triangle related?

Circle Formulas C = π  d A = π  r ²

Find the circumference and area of the circles below. C = π  d C = 3.14  6 C = cm A = π  r ² A = 3.14  9 A = cm² 9 cm C = π  d C = 3.14  18 C = cm A = π  r ² A = 3.14  81 A = 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 cm C = π  d C = 3.14  24 C = cm A = π  r ² A = 3.14  144 A = cm² C = π  d C = 3.14  6 C = cm A = π  r ² A = 3.14  9 A = 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 = π  d C = 3.14  32 C = cm A = π  r ² A = 3.14  256 A = cm² 8 cm C = π  d C = 3.14  8 C = 25.12cm A = π  r ² A = 3.14  16 A = 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 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 = π  d C = 29π That 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 = π  d A = π  r ²

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  r ² A =

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

3 in Find the area of the outermost region in the circle below. A = π  r ²

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