GM5-4: Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.

Elaboration on this Achievement Objective

This means that students should find the ratio of the diameter of a circle to its perimeter (π) by measuring several circles and looking for the relationship.

They should understand that the formula for the circumference of a circle can be expressed in two ways:
C = 2πr (2 times pi times the radius), or
C = πD (pi times the diameter)


They should apply the formula to find the circumference of any circle, for example the circumference of a bicycle tyre. Students should find the formula for area of a circle by cutting several circles into increasingly small sectors and reassembling the sectors to approximate rectangles, A = πr2 (pi times the radius squared). They should apply this formula to finding the area of any circle.

Students will find the perimeters of composite shapes by adding the lengths of the sides together. At Level Five composite shapes are made up of common polygons (for example rectangles, triangles, semicircles). Students will find the area of composite shapes by calculating the areas of the parts and adding them together. Students will find the volumes of prisms by multiplying the area of their cross section by their length, for example for a cylinder multiply the area of the circle by the length of the cylinder.