Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving determining radius, diameter, circumference and area from each other (VCMMG288)

LO: To investigate the features of circles such as circumference, area, radius and diameter and to solve real-world problems.



Know:

  • the properties and features of circles.

  • the definition of key terminology that involves circles eg.) circumference, radius, diameter and area.

Understand:

  • That formulas can be used to quickly and efficiently to determine the features (area and circumference) of a circle.

Do:

  • I can identify the different features of a circle and utilise formulas to find the properties of a circle.

Elaborations:

  • demonstrate an understanding of circles by:

    • describing the relationships among radius, diameter, and circumference.
    • relating circumference to pi
    • constructing circles with a given radius or diameter
    • solve problems involving the radii, diameters and circumferences of circles.

Features of Circles

Diameter of a Circle

A diameter of a circle is the distance from one side of a circle to the other side of a circle. It splits a circle into 2 equal pieces.

Radius of a Circle

A radius of a circle is the distance from the center of the circle to the edge.

Circumference of a Circle

Circumference is essentially the perimeter of a circle or the distance around the outside of the circle.

Formulas for Finding Features of Circles

Formula for Finding the Circumference of a Circle.

There are 2 formulas for finding the circumference of a circle, they both work out to give you the same answer:

C = ∏ x d
Circumference = Pi x diameter

C = 2 x ∏ x r
Circumference = Pi x radius

Remember the radius of a circle is exactly half of the diameter of a circle, which is why the diameter is = to 2r.


Area of a Circle

Area of a circle is the amount of space that the inside of the circle occupies.

Formula for finding the area of a circle:

A = ∏ x r x r
Area = Pi x r^2

Problem Solving Tasks

  • Use string to measure the circumferences and the diameters of a variety of cylindrical cans, and investigate the ratio of the circumference to the diameter.

  • solve problems involving the estimation and calculation of the circumference and the area of a circle.

Features of Circles Videos

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