Chapter 10 Surface Area and Volume

WORK PROGRAM

Chapter 10 Surface area and volume

Strand: Measurement

Substrands and outcomes:

LengthMS3.1Selects and uses the appropriate unit and device to measure lengths, distances and perimeters

Perimeter and areaMS4.1Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circlesand figures

composed of rectangles and triangles

Perimeter and areaMS5.1.1Uses formulae to calculate the area of quadrilaterals and finds areas and perimeters of simple

composite figures

Perimeter and areaMS5.2.1Finds areas and perimeters of composite figures

Surface area and volumeMS4.2Calculates surface area of rectangular and triangular prisms and volume of rightprisms and

cylinders

Surface area and volumeMS5.2.2Applies formulae to find the surface area of right cylinders and volumes of right pyramids, cones

and spheres and calculates the surface area and volume of composite shapes

Surface area and volumeMS5.3.1Applies formulae to find the surface area of pyramids, right cones and spheres

1

• calculating perimeters of squares, rectangles and triangles

• using formulas to calculate the circumference of circles
• using formulas for the area of a square and rectangle
• using the formula for the area of a triangle
• using the formula to calculate the area of circles
• converting between metric units of length
• converting between metric units of area

• calculating the surface area of rectangular prisms
• calculating the surface area of triangular prisms
• calculating the volume of prisms with cross-sections that are rectangular
• calculating the volume of prisms with cross-sections that are triangular
• using the formula to find the volume of cylinders

• calculating the perimeter of simple composite figures consisting of two shapes including quadrants and semicircles
• dissecting composite shapes into simpler shapes (Applying strategies)

• calculating the perimeter of sectors
• calculating the perimeter of composite figures by dissection into triangles, special quadrilaterals, semicircles and sectors
• solving problems involving perimeter of composite shapes (Applying strategies)
• applying formulae and properties of geometrical shapes to find perimeters (Applying strategies)

• developing and using formulae to find the area of quadrilaterals
• calculating the area of simple composite figures consisting of two shapes including quadrants and semicircles
• selecting and using the appropriate formula to calculate the area of a quadrilateral (Applying strategies)
• dissecting composite shapes into simpler shapes (Applying strategies)
• solving practical problems involving area of quadrilaterals and simple composite figures (Applying strategies)

• calculating the area of sectors
• calculating the area of composite figures by dissection into triangles, special quadrilaterals, semicircles and sectors
• solving problems involving area of composite shapes (Applying strategies)
• calculating the area of an annulus (Applying strategies)
• applying formulae and properties of geometrical shapes to find areas (Applying strategies)

• developing a formula to find the surface area of right cylinders
• finding the surface area of right cylinders

• finding the dimensions of solids given their surface area by substitution into a formula to generate an equation

Maths Quest challenge: Q1-2 (page 420)

• calculating the surface area of composite solids involving right cylinders and prisms
• solving practical problems related to surface area (Applying strategies)

• identifying the perpendicular and slant height of pyramids and right cones
• using Pythagoras’ theorem to find slant height, base length or perpendicular height of pyramids and right cones
• devising and using methods to calculate the surface area of pyramids
• developing and using the formula to calculate the surface area of cones
• using the formula to calculate the surface area of spheres
• finding the dimensions of solids given their surface area by substitution into a formula to generate an equation

• using the fact that a pyramid has one-third the volume of a prism with the same base and the same perpendicular height
• using the fact that a cone has one third the volume of a cylinder with the same base and the same perpendicular height
• using the formula to find the volume of pyramids and cones where A is the base area and h is the perpendicular height
• using the formula to find the volume of spheres where r is the length of the radius
• finding the dimensions of solids given their volume by substitution into a formula to generate an equation
• finding the volume of prisms whose bases can be dissected into triangles, special quadrilaterals and sectors
• finding the volume of composite solids
• solving problems relating to volumes of right pyramids, cones and spheres (Applying strategies)
• solving practical problems related to volume and capacity (Applying strategies)

1