CIRCLES... All you ever wanted to know about circles...until grade 8! Make the world go round.

What you will need... In this unit you will need the following: A) A compass B) A protractor C) Your workbook D) Your textbook E) Your binder

What you will learn... You will learn to: Investigate and explain the relationship between radius, diameter and circumference. Determine the sum of the central angles of a circle. Construct circles and solve problems involving circles. Develop formulas to find areas of shapes. Draw, label and interpret circle graphs.

Today’s Notes – January 22nd Title of the Notes: 4.1 Investigating Circles

Radius (Radii) The distance from the center of a circle to any point along the circle. Radii

Diameter The distance across a circle, measured through its center.

Task... Take out a sheet of paper... Using a compass draw a large circle.

Using a ruler draw a line through the center of your circle. Measure the line segment.

Label the line segment with its length. Example: 6.2 cm

Draw two segments off the line going through the center.

Measure the two line segments you just drew. Write the measurement beside each line.

Your two smaller line segments should be equal in length. Why would that be?

Finding the Radius The radius is ALWAYS half of the diameter. Therefore: r = d ÷ 2 Radius Diameter

If r = d ÷ 2 and d is = 9 mm, what is r equal to? Therefore, the radius is 4.5 mm.

Finding the Diameter Diameter is equal to d = 2r What would the value of d be if r = 2 cm? 2 cm

d = 2r and r = 2 cm Therefore d = 2(2) 2 x 2 = 4 cm Diameter is equal to 4 or d = 4 cm

A word problem for you A circular tabletop is to be cut from a rectangular piece of wood that measures 2 meters by 3 meters. What is the radius of the largest tabletop that could be cut? Explain your answer and draw a picture to demonstrate that you understand.

Which rectangle length is the longest? 3 meters 2 meters

What is half of the shortest side? 2 is the length of shortest side. Therefore, half of the shortest side is 1. The radius of the largest tabletop would be 1 meter.

Your Task... Use a compass to construct the following circles... A) a radius of 5 cm B) a diameter of 10 cm C) a radius of 7 cm D) a diameter of 6 cm

Homework Textbook Page 131-132 #1-6 Workbook Page 78-81 Worksheets All due next class. Worksheets will be handed in and a 20 mark homework check will be done in class.

Circumference

Л (Pi...my favourite desert)

Irrational Number

Base

Height

Circle Graph

Sector

Legend

Percent Circle

Central Angle

Sector Angle

Pie Chart...desert AGAIN!