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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)

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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.

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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.

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Features of Circles

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Diameter of a Circle

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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.

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Radius of a Circle

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

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Circumference of a Circle

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

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Formulas for Finding Features of Circles

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Formula for Finding the Circumference of a Circle.

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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.

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Area of a Circle

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

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Formula for finding the area of a circle:

A = ∏ x r x r
Area = Pi x r^2

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Problem Solving Tasks

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  • 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.

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Features of Circles Videos

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