Investigating Circles

Properties of Circles

• Circle  radius diameter A closed curved with all points the same distance from center •  origin area circumference

Origin The origin is the center of the circle. origin All points on a circle are the same distance from the origin. A circle is named by its center. Name: Circle A origin A

Diameter The diameter is the distance of a line segment going across a circle through its center. AB It divides the circle exactly in half. Is viewed as a line of symmetry. Symbol is lower case d. diameter

Radius Radius is the distance from the center of the circle to any point on the circle. Radius is one-half the length of the diameter. Symbol is lower case r.

Circumference Circumference refers to the total distance around the outside of a circle. Can also be called the perimeter of a circle. Symbol is an upper case C.

Diameter, Radius, Circumference of a Circle

Diameter, Radius, Circumference of a Circle

Making Connections You can estimate the age of a tree by measuring the circumference of a tree. For many kinds of trees, each 2 cm represents one year of growth. 100 cm

Making Connections An odometer is an instrument used to measure the distance a vehicle travels by counting the number of wheel revolutions.

Properties of a Circle – Internet Activity SITE: www. harcourtschool Properties of a Circle – Internet Activity SITE: www.harcourtschool.com SELECT: Math / Grade 7 / Glossary For each word given, write a definition and illustrate an example. Record work neatly and space between each definition. title and date your page Subtitle – Properties of a Circle (underline) When you finish, go to site www.aplusmath.com Select Games, then the 1st Geometry Version of Non-Java Games. Words to Define circle, circumference, diameter, radius Tools Required pencil, eraser, ruler, red pen, disc, looseleaf

Circle Properties closed curved all points same distance from centre (origin) radius diameter circumference area pi

Concepts you Should Now Know Origin Diameter Radius Circumference Ratio of C & d center of a circle distance across center of circle (d) half the distance of diameter (r) distance around the outside of a circle ( C ) Circumference is actually 3.14 ( ) bigger than the diameter or about 3 times bigger

Diameter, Radius, Circumference of a Circle

Ratio Of The Circumference Of A Circle To Its Diameter If you measure the distance around a circle (C) and divide it by the distance across the circle through its center (d), you should always come close to a particular value We use the Greek letter  to represent this value.  (pi)

Ratio Of The Circumference Of A Circle To Its Diameter The value of  is approximately 3.14159265358979323. . . So, C/d always = ___ Using  is a quicker way to find the circumference of a circle. Using  allow us to calculate circumference with less measuring,  (pi)

How  Helps Knowing the value of ,allows us to use formulas to calculate circumference. If the diameter of a circle is 2 cm, how could you calculate the circumference? C =  x ___ Estimate the circumference The circumference is ____ 2cm

Circumference of a Circle  C = x d C = 3.14 x 3 C = 9.42cm If the diameter is 3cm

Circumference of a Circle Estimate Is . . .  C = x d C = 3.14 x 1.5 C = 4.71cm If the diameter is 1.5cm

Circumference of a Circle C =  x d …but we don’t know the diameter  C = x d d = 2 x r d = 2 x 3 d = 6 C = 3.14 x 6 C = 18.84m If the radius is 3m

Circumference of a Circle  C = x d C = 3.14 x 5 C = 15.7 Estimate is . . If the diameter is 5

What formula could I use? What is the diameter of a circle if the circumference is 18.8?

What is the diameter of a circle if the circumference is 13.2?

What is the diameter of a circle if the circumference is 33.9?

Area of a Circle

Estimate the area of this circle. Area of a Circle Estimate the area of this circle.

Area of a Circle Seeing the square units can help. Remember each block is one square unit Estimate is

Area of a Circle Counting square units can give you a good estimate, however, can be time consuming. Counting will not always give an exact answer. Actual is The formula for finding the area of a circle is A =  x r x r or  r2 Estimate is

Pie are square? NO, pie are round!

Area of a Circle Estimated area is Remember A =  x r x r or  r2 Actual area is