This course extends mensuration to the shapes met in higher classes. You find the area of any triangle from its three sides with Heron's formula, and of quadrilaterals by splitting them into triangles. You measure parts of circles: arcs, sectors, segments and rings. Then you work in three dimensions, finding surface areas and volumes of cuboids, cubes, cylinders and hollow pipes, right circular cones, spheres and hemispheres, with units of capacity in litres. The course ends with combined solids such as toys and capsules, and with recasting problems where a solid is melted or earth is dug out but the volume stays the same.
Middle Years
Mensuration (Level 2)
Areas and volumes beyond the basics: Heron's formula, arcs, sectors and segments of circles, and the surface areas and volumes of cuboids, cylinders, cones, spheres and solids built from them.
- 7 lessons
Overview
Lessons
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Heron's formula
The area of a triangle from its three sides using the semi-perimeter, special cases for isosceles and equilateral triangles, and areas of quadrilaterals.
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Arcs, sectors and segments
Circumference and area of a circle, the length of an arc, areas of sectors, minor and major segments, and rings between two circles.
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Surface area of cuboid, cube and cylinder
Total and lateral surface areas of cuboids and cubes, the diagonal of a box, and curved and total surface areas of a cylinder, with painting and rolling problems.
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Volume of cuboid, cube and cylinder
Units of volume and capacity, volumes of cuboids, cubes, cylinders and hollow pipes, and counting bricks for a wall.
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The right circular cone
Radius, height and slant height of a cone, its curved and total surface areas, and its volume, one third of the matching cylinder.
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Sphere and hemisphere
Surface area and volume of a sphere and a hemisphere, finding the radius from them, and how area and volume change when the radius changes.
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Combined solids and recasting
Surface areas and volumes of toys, capsules and tents made of simple solids, and problems where a solid is melted and recast or earth is dug and spread.