Measurement and Geometry
Outcomes
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Volume
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MA5.3-14MG
Applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids
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Solve problems involving the volumes of right pyramids, right cones, spheres and related composite solids (ACMMG271)
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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
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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
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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
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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
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Solve problems involving the volumes of right pyramids, right cones, spheres and related composite solids (ACMMG271)
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MA5.3-14MG
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Circle Geometry
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MA5.3-17MG
Applies deductive reasoning to prove circle theorems and to solve related problems
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Prove and apply angle and chord properties of circles (ACMMG272)
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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
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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
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Apply chord and angle properties of circles to find unknown angles and lengths in diagrams
Examples
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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
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Prove and apply angle and chord properties of circles (ACMMG272)
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MA5.3-17MG