Chapter 11.1
Area of compound shapes
Break down complex shapes into rectangles and triangles; calculate total area systematically.
Chapters12
Compound shapes, 3D measurements, volume calculations, problem-solving.
Time invested10 hrs
Approximate guided learning.
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Chapter 11.2
Perimeter of compound shapes
Find total perimeter of shapes combining straight edges; handle missing dimensions.
Chapter 11.3
Arc length and sector area
Use radian and degree measures; apply sector and segment formulas efficiently.
Chapter 11.4
Surface area of pyramids
Find base and triangular face areas; use Pythagoras for slant height when needed.
Chapter 11.5
Surface area of cones
Calculate base and lateral surface areas; relate to sector area of unrolled net.
Chapter 11.6
Surface area of spheres
Apply the formula 4πr²; solve for radius given surface area.
Chapter 11.7
Volume of pyramids
Use V = (1/3) × base area × height; distinguish height from slant edge.
Chapter 11.8
Volume of cones
Apply V = (1/3)πr²h; relate to cylinder volume ratio.
Chapter 11.9
Volume of spheres
Use V = (4/3)πr³; solve for radius or diameter given volume.
Chapter 11.10
Frustums
Calculate volume and surface area of cone/pyramid frustums via subtraction.
Chapter 11.11
Compound 3D shapes
Decompose complex solids; combine volumes or surface areas of component shapes.
Chapter 11.12
Area and volume problem-solving
Apply all techniques to real-world and GCSE exam contexts; optimise design scenarios.
Next steps
Mastered 2D and 3D measurement? Review Section 10, or progress to Section 12 for trigonometry and advanced geometry.