# 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

Section /**GC tips, Investigations,**

**History of mathematics, Maths Quest challenge, 10 Quick Questions,**

Code puzzles,

Career profiles /

**SkillSHEETs, WorkSHEETs, Interactive games, Testyourself, Topic tests**

(CD-ROM) /

**Technology applications**

(CD-ROM) /

**Learning outcomes**

1

Are you ready? (page 392) / SkillSHEETs (page392)10.1: Perimeter of squares, rectangles, triangles and circles

10.2: Area of squares, rectangles, triangles and circles

10.3: Converting length and area units

10.4: Surface area of cubes and rectangular prisms

10.5: Surface area of triangular prisms

10.7: Volume of cubes and rectangular prisms

10.8: Volume of triangular prisms

10.9: Volume of cylinders / MS3.1

- 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

Perimeter (page 393)

WE 1a-c, 2a-b, 3, 4

Ex 10A Perimeter (page396) / Maths Quest challenge: Q1-2 (page 398) / SkillSHEET 10.1: Perimeter of squares, rectangles, triangles and circles (page 396) / GC program Casio: Measurement (page 396)

GC program TI: Measurement (page 396)

Mathcad: Perimeter (page396)

Excel:Length converter (page 396)

Excel: Perimeter and area (page 396)

Cabri geometry:Circumference and area of a circle (page 396) / MS5.1.1

- 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)

Area (page 399)

WE 5a-b, 6a-b

Ex 10B Area (page 403) / SkillSHEET 10.2: Area of squares, rectangles, triangles and circles (page 403)

SkillSHEET 10.3: Converting length and area units (page 405)

Game time 001(page 405)

WorkSHEET 10.1 (page405) / Excel:Area converter (DIY) (page 399)

Mathcad: Area (page 403)

GC program Casio:Measurement (page 403)

GC program TI: Measurement (page 403)

Excel:Perimeter and area (page 403)

Cabri geometry:Area of a sector (page 404) / MS5.1.1

- 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)

Surface area (page 406)

WE 7, 8a-b

Ex 10C Surface area (page409) / 10 Quick Questions 1 (page 410) / SkillSHEET 10.4: Surface area of cubes and rectangular prisms (page409)

SkillSHEET 10.5: Surface are of triangular prisms (page 409) / Mathcad:Surface area (page 409)

Excel: Surface area and volume (page 409)

GC program Casio: Measurement (page 409)

GC program TI: Measurement (page 409) / MS5.2.2

- 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

Surface area of spheres, cones and composite solids (page 411)

WE 9, 10, 11, 12, 13, 14ab

Ex 10D Surface area of spheres, cones and composite solids (page417) /

### Maths Quest challenge: Q1-2 (page 420)

Code puzzle (page 421) / WorkSHEET 10.2 (page420) / Mathcad:Surface area of a sphere (page 417)Mathcad: Surface area (page 417)

Excel:Surface area and volume (page 417)

GC program Casio: Measurement (page 417)

GC program TI: Measurement (page 417) / MS5.2.2

- 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

Volume (page 422)

WE 15a-b, 16, 17a-b, 18

Ex 10E Volume (page426) / Investigation: Comparing volumes of pyramids and prisms (page 424)

Maths Quest challenge: Q1-2 (page 428)

Investigation: More units of measurement (page428)

Investigation:Water tank worries (page 429)

10 Quick Questions 2 (page 429)

Career profile: Mike Matheson (page 430) / SkillSHEET 10.6: Converting volume units (page 422)

SkillSHEET 10.7: Volumes of cubes and rectangular prisms (pages422, 426)

SkillSHEET 10.8: Volume of triangular prisms (page 426)

SkillSHEET 10.9: Volume of cylinders (page 426)

Game time 002(page 428)

WorkSHEET 10.3 (page428) / Excel:Surface area and volume (page 427)

Mathcad: Volume (page427)

GC program Casio: Measurement (page 427)

GC program – TI: Measurement (page 427) / MS5.2.2

- 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)

Summary (page 431)

Chapter review (page 432) / ‘Test yourself’ multiple choice questions

Topic tests (2)

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