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 -8 + 6n -9 5) The formula for the area of a triangle is ______. 90º 180º Mean absolute deviation 4n - 17

Warm Up 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? 12y - 5 - n -7y - 3 + 8n A = Πr² A = 3.14 (5)² A = 78.5 ft² 7n + 5y -8

2a + 8 units 2a + 4 units² Perimeter is 12 units Area is 8 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/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 = πd A = πr²

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? _______ 3 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  18 C = 56.52 cm A = πr² A = 3.14  81 A = 254.34 cm² 3 9

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? _______ 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 4 16

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 = πd C = 3.14  8 C = 25.12cm A = πr² A = 3.14  16 A = 50.24 cm² C = πd C = 3.14  32 C = 100.48 cm A = πr² A = 3.14  256 A = 803.84 cm² 4 16

Circumference doubles, but the area quadruples. 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.

That means the diameter is 29 in. Therefore, the radius is 14.5 in. 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.

A = πr² C = πd A = 3  81 54ft = 3  d A = 243 ft² 18 ft = d 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 = πr² A = 3  81 A = 243 ft² C = πd 54ft = 3  d 18 ft = d

Mary wants to cover the top of a circular pillow with fur 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

C = πd C= 3.14  24 in C= 75.36 in 75.36 inches  50 = 3768 inches 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.

A = πr² A = 3.14  81 A = 254.34 in² A = πr² A = 3.14  36 Find the area of the outermost region in the circle below. A = πr² A = 3.14  81 A = 254.34 in² 3 in 3 in 3 in 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 C = 3.14  2(3.39) C = 21.2892 inches Approximately 21 inches = 11.46 r = 11.46 r = 3.39 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