About this topic
Before you begin
Calculate composite areas, exposed surfaces and volumes in G3 Mathematics, choosing matching degree or radian measures for circular regions.
Learning goals
- Convert between square centimetres and square metres
- Convert between cubic centimetres and cubic metres
- Calculate the area of a parallelogram
- Calculate the area of a trapezium
- Calculate and justify area and perimeter
- Convert compatible measurement units
- Calculate the area of a circle from a given radius or diameter
- Calculate the circumference of a circle from a given radius or diameter
- Calculate the volume of a cube or cuboid
- Calculate the total surface area of a cube or cuboid
- Calculate a right prism's volume from its cross-section and perpendicular length
- Calculate a right prism's exposed area with the stated end faces
- Calculate the volume of a right circular cylinder
- Calculate cylinder area with the stated circular end faces
- Calculate and justify volume and surface area
- Calculate pyramid volume from base area and perpendicular height
- Calculate a right square pyramid's exposed area from its face slant height
- Calculate a right circular cone's volume from perpendicular height
- Calculate a right circular cone's exposed area from its slant height
- Calculate the volume of a sphere
- Calculate the surface area of a sphere
- Calculate the volume of a hemisphere
- Calculate hemisphere area with or without its flat base
- Calculate arc length from a degree angle
- Calculate sector area from a degree angle
- Calculate a complete sector perimeter from a degree angle
- Calculate circle, arc, sector and segment measures
- Calculate arc length from a radian angle
- Calculate sector area from a radian angle
- Calculate a complete sector perimeter from a radian angle
- Convert a degree angle to exact radians
- Convert an exact multiple of pi radians to degrees
- Calculate the area of a minor or major segment of a circle from its radius and central angle
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)
Choose a lesson
Work through them in order.
- Not startedUnits, heights and composite areaNextConvert squared and cubed units, then use perpendicular heights and non-overlapping regions to calculate area.
- Not startedCircles and composite boundariesNextUse the radius for circle area and trace every part of a composite boundary.
- Not startedCuboids and liquid volumeNextUse complete layers to derive cuboid volume and measure liquid in a rectangular tank.
- Not startedPrisms, cylinders and exposed surfacesNextSeparate cross-sectional area, perpendicular length, volume and the surfaces actually exposed.
- Not startedPyramids, cones and spheresNextDistinguish perpendicular height, slant height and radius when using volume and surface-area formulae.
- Not startedDegree sectors and arc lengthsNextUse the sector’s share of a full turn and distinguish an arc from the complete sector perimeter.
- Not startedRadians, sectors and segmentsNextUse radian measure consistently and subtract a triangle only for the matching segment.
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