Area, volume and mensuration
Build and connect the representations and methods in area, volume and mensuration.
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Before you begin
Build and connect the representations and methods in area, volume and mensuration.
Learning goals
- Calculate and justify area and perimeter
- Convert compatible measurement units
- Calculate and justify volume and surface area
- Calculate circle, arc, sector and segment measures
Syllabus statements covered
- area of triangle as ½ × base × height • area and circumference of circle • area of parallelogram and trapezium • problems involving perimeter and area of composite plane figures • volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere • conversion between cm^2 and m^2, and between cm^3 and m^3 • problems involving volume and surface area of composite solids • arc length as fraction of the circumference and sector area as fraction of the area of a circle
- area of triangle as ½ × base × height
- area and circumference of circle
- area of parallelogram and trapezium
- problems involving perimeter and area of composite plane figures
- volume and surface area of cube and cuboid
- conversion between cm² and m², and between cm³ and m³
- problems involving volume and surface area of composite solids
- volume and surface area of prism and cylinder
- conversion between cm² and m², and between cm³ and m³
- volume and surface area of pyramid, cone and sphere
- conversion between cm² and m², and between cm³ and m³
- arc length and sector area as fractions of the circumference and area of a circle
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Units, heights and composite areaG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020 · Normal (Technical) Secondary 3–4 Mathematics 2022Convert squared and cubed units, then use perpendicular heights and non-overlapping regions to calculate area.
- Circles and composite boundariesG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Use the radius for circle area and trace every part of a composite boundary.
- Cuboids and liquid volumeG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Use complete layers to derive cuboid volume and measure liquid in a rectangular tank.
- Prisms, cylinders and exposed surfacesG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Separate cross-sectional area, perpendicular length, volume and the surfaces actually exposed.
- Pyramids, cones and spheresG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Distinguish perpendicular height, slant height and radius when using volume and surface-area formulae.
- Degree sectors and arc lengthsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Use the sector’s share of a full turn and distinguish an arc from the complete sector perimeter.
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