HEATHCOTE HIGH SCHOOL
YEAR 10 MATHEMATICS PROGRAM
2006
TOPIC:
Surface Area and Volume
SUGGESTED TIME:
CONTENT
Key Ideas for Stage 4
1. Find the surface area of rectangular and
triangular prisms
2. Find the volume of right prisms and cylinders
3. Convert between metric units of volume
OUTCOMES:
Stage 4: MS4.2 Calculates surface area of rectangular and triangular prisms and volume of right prisms and cylinders
(p 131)
Stage 5.2: MS5.2.2 Applies formulae to find the surface area of right cylinders and volume of right pyramids, cones and
spheres and calculates the surface area and volume of composite solids (p 132)
Stage 5.3: MS5.3.1 Applies formulae to find the surface area of pyramids, right cones and spheres (p 133)
KNOWLEDGE AND SKILLS
 identifying the surface area and edge lengths
of rectangular and triangular prisms
 finding the surface area of rectangular and
triangular prisms by practical means eg from
a net
 calculating the surface area of rectangular
and triangular prisms
 converting between units of volume
 using the kilolitre as a unit in measuring large
volumes
 constructing and drawing various prisms from
a given cross-sectional diagram
 identifying and drawing the cross-section of
a prism
 developing the formula for volume of prisms
by considering the number and volume of
layers of identical shape
 calculating the volume of a prism given its
perpendicular height and the area of its
cross-section
RESOURCES
New Century 10 Advanced Ch
New Century 10 Intermediate
Ch
Maths Works 10 Intermediate
Ch
Spectrum 10 Standard Ch
New Century 9 Advanced Ch
New Course Mathematics 9
Advanced Ch
New Century 9 Intermediate Ch
Maths Works 9 Intermediate Ch
Spectrum 9 Standard Ch
TERMINOLOGY
area, surface, volume, formulae,
prisms, pyramids, capacity, milli,
kilo, mega, right figures,
composite solids, spheres, cones,
edges, net, cross section,
perpendicular, slant, dissection,
cylinders, quadrilaterals, sectors,
intervals, Pythagoras Theorem
New Century 10 Adv & Int BLM
Excel 10 Advanced
New Century 9 Adv & Int BLM
Excel 9 Advanced
Excel 8 Workbook 1
Excel 8 Workbook 2
Literacy in Maths Book
 calculating the volume of prisms with crosssections that are rectangular and triangular
 calculating the volume of prisms with crosssections that are simple composite figures
that may be dissected into rectangles and
triangles
 developing and using the formula to find the
volume of cylinders
Heathcote High School
533568763
Page 1 of 3
Key Ideas for Stage 5.2
1. Find surface area of right cylinders and
composite solids
2. Find the volume of right pyramids, cones,
spheres and composite solids
 developing a formula to find the surface area
of right cylinders
 finding the surface area of right cylinders
 calculating the surface area of composite
solids involving right cylinders and prisms
 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
 using the formula to find the volume of
spheres
 finding the dimensions of solids given their
volume and/or surface area 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
Key Ideas for Stage 5.3
 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
 establishing and applying the fact that in two
similar figures with similarity ratio 1: k
1. Apply formulae for the surface area of
pyramids, right cones and spheres
2. Explore and use similarity relationships for
area and volume
Heathcote High School
533568763
WORKING
MATHEMATICALLY
DIAGNOSIS/ASSESSMENT
 recognise, giving examples,
that prisms with the same
volume may have different
surface areas, and prisms
with the same surface area
may have different volumes
(Reasoning, Applying
Strategies)
 solve practical problems
related to surface area eg
compare the amount of
packaging material needed
for different shapes (Applying
Strategies
 apply Pythagoras’ theorem to
problems involving surface

Page 2 of 3




Heathcote High School
-
matching angles have the same size
matching intervals are in the ratio 1: k
matching areas are in the ratio 1: k2
matching volumes are in the ratio 1: k3
533568763
area (Applying Strategies)
 solve problems involving the
similarity ratio and areas and
volumes (Applying
Strategies)
Page 3 of 3