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STAGE 5.3 - MEASUREMENT AND GEOMETRY (Area and surface area (Lesson 2:…
STAGE 5.3 - MEASUREMENT AND GEOMETRY
AREA AND SURFACE AREA
Solve problems involving the surface areas of right pyramids, right cones, spheres and related composite solids (ACMMG271)
identify the 'perpendicular heights' and 'slant heights' of right pyramids and right cones
apply Pythagoras' theorem to find the slant heights, base lengths and perpendicular heights of right pyramids and right cones
devise and use methods to find the surface areas of right pyramids
develop and use the formula to find the surface areas of right cones:
Curved surface area of cone=πrl where r is the length of the radius and l is the slant height
use the formula to find the surface areas of spheres:
Surface area of a sphere=4πr2 where r is the length of the radius
solve a variety of practical problems involving the surface areas of solids
find the surface areas of composite solids, eg a cone with a hemisphere on top (Problem Solving)
find the dimensions of a particular solid, given its surface area, by substitution into a formula to generate an equation (Problem Solving)
Volume
Solve problems involving the volumes of right pyramids, right cones, spheres and related composite solids (ACMMG271)
develop and use the formula to find the volumes of right pyramids and right cones:
use the formula to find the volumes of spheres:
find the volumes of composite solids that include right pyramids, right cones and hemispheres,
solve a variety of practical problems relating to the volumes and capacities of right pyramids, right cones and spheres
Area and surface area
Lesson 1. Pyramids
What is a pyramid
Slant height compared to perpendicular height + pythag
Surface Area of a pyramid.
Lesson 2: Cones
What is a cone.
Slant height calculations (compare with pyramid
SA formula derivation SA=πrl
SA calculation
E4E: Frustrum of a cone
Lesson 3. SA of a sphere
Here's the formula remember it and use it.
Hemisphere SA
Lesson 4: Composite shapes
Mirror year 10 version but with spheres cones and pyramids thrown in
Volume
Lesson 1: Volume of a pyramid.
Formula derivation
Identify that the V of a pyramid = 1/3 of a prism with same dimensions
Calc V of pyramids (inc. pythagoras questions)
Lesson 2: Volume of a cone
V of cone=1/3 V of Cylinder
Calc V of Cone (inc. pythagoras questions)
Formula derivation
Lesson 3: Volume of a sphere
Introduce formula
Calc V of Sphere
Calc V of Hemisphere
Lesson 4: Volume of composite shapes
V of comp shapes with 1 shape added to another
V of comp shapes with 1 shape subtracted from another
Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271)
using formulas to solve problems
using authentic situations to apply knowledge and understanding of surface area and volume