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 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, sector area and area of a segment of a circle • use of radian measure of angle (including conversion between radians and degrees)
- area of parallelogram and trapezium
- problems involving perimeter and area of composite plane figures
- volume and surface area of prism and cylinder
- conversion between cm² and m² , and between cm³ and m³
- problems involving volume and surface area of composite solids
- volume and surface area of pyramid, cone and sphere
- arc length, sector area and area of a segment of a circle
- use of radian measure of angle (including conversion between radians and degrees)
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 areaG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Convert squared and cubed units, then use perpendicular heights and non-overlapping regions to calculate area.
- Circles and composite boundariesG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Use the radius for circle area and trace every part of a composite boundary.
- Cuboids and liquid volumeG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Use complete layers to derive cuboid volume and measure liquid in a rectangular tank.
- Prisms, cylinders and exposed surfacesG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Separate cross-sectional area, perpendicular length, volume and the surfaces actually exposed.
- Pyramids, cones and spheresG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Distinguish perpendicular height, slant height and radius when using volume and surface-area formulae.
- Degree sectors and arc lengthsG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Use the sector’s share of a full turn and distinguish an arc from the complete sector perimeter.
- Radians, sectors and segmentsG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Use radian measure consistently and subtract a triangle only for the matching segment.
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