Measurement and Geometry
Outcomes

Volume

MA5.314MG
Applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids

Solve problems involving the volumes of right pyramids, right cones, spheres and related composite solids (ACMMG271)

Develop and use the formula to find the volumes of right pyramids and right cones:
Volume of pyramid / cone = 1/3Ah where A is the base area and h is the perpendicular height CCT
Examples

Use the formula to find the volumes of spheres:
Volume of sphere = 4/3 pi r cubed where r is the length of the radius
Examples

Find the volumes of composite solids that include right pyramids, right cones and hemispheres,
eg find the volume of a cylinder with a cone on top
Examples

Develop and use the formula to find the volumes of right pyramids and right cones:
Volume of pyramid / cone = 1/3Ah where A is the base area and h is the perpendicular height CCT

Solve problems involving the volumes of right pyramids, right cones, spheres and related composite solids (ACMMG271)

MA5.314MG

Circle Geometry

MA5.317MG
Applies deductive reasoning to prove circle theorems and to solve related problems

Prove and apply angle and chord properties of circles (ACMMG272)

prove the following chord properties of circles: CCT
chords of equal length in a circle subtend equal angles at the centre and are equidistant from the centre
the perpendicular from the centre of a circle to a chord bisects the chord; con
Examples

prove the following angle properties of circles: CCT
the angle at the centre of a circle is twice the angle at the circumference standing on the same arc
the angle in a semicircle is a right angle
angles at the circumference, standi
Examples

Apply chord and angle properties of circles to find unknown angles and lengths in diagrams
Examples

prove the following chord properties of circles: CCT
chords of equal length in a circle subtend equal angles at the centre and are equidistant from the centre
the perpendicular from the centre of a circle to a chord bisects the chord; con
 Prove and apply tangent and secant properties of circles

Prove and apply angle and chord properties of circles (ACMMG272)

MA5.317MG