Core Mensuration

Topics

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Sample objectives

What this unit covers

• Units of measure: Understand and apply metric units for mass, length, area, volume, and capacity in real-life contexts, and be able to convert quantities between larger and smaller metric units. This includes units such as mm, cm, m, km for length; mm², cm², m², km² for area; mm³, cm³, m³ for volume; ml, l for capacity; and g, kg for mass. Additionally, be able to convert between different area units (e.g., cm² to m²) and between volume and capacity units (e.g., m³ to litres).
• Area and perimeter: Perform calculations related to the perimeter and area of shapes, including rectangles, triangles, parallelograms, and trapeziums, with the exception of the area formula for triangles, which is not provided.
• Circles, arcs and sectors: Perform calculations related to the circumference and area of a circle, with answers potentially expressed in terms of π. The necessary formulas are provided in the List of formulas. Additionally, calculate the arc length and sector area as fractions of the circle's circumference and area, given that the sector angle is a divisor of 360°.
• Surface area and volume: Perform calculations and solve problems related to the surface area and volume of various shapes, including cuboids, prisms, cylinders, cones, spheres, and pyramids. Answers may be expressed in terms of π. The relevant formulas include those for the curved surface area and volume of these solids, as well as the surface area of a sphere. A prism is defined as any solid with a consistent cross-section, such as a cylindrical sector.
• Compound shapes and parts of shapes: Perform calculations and solve problems related to the perimeters and areas of both compound shapes and sections of shapes, with answers potentially expressed in terms of π. Additionally, perform calculations and solve problems concerning the surface areas and volumes of both compound solids and sections of solids, such as determining the volume of half a sphere.