Prior Content: Prisms, 2D Area & Perimeter, Manipulating Formulae/ Changing the Subject, Forming Equations, Algebraic Proof, Compound Measures, Upper & Lower Bounds, Circles & Sectors, Pythagoras
Possible Next Steps:
Contents
- 1.1 Names & Labelling 3D Shapes
- 1.2 Drawing 3D Shapes with Isometric Paper
- 1.3 Viewing Angles: Drawing from a Given Shape
- 1.4 Viewing Angles: Drawing Shapes from Given Viewing Angles
- 2.1 Nets of 3D Shapes
- 3.1 Spheres & Hemispheres
- 3.2 Pyramids
- 3.3 Compound Shapes
- 4.1 Working with Formulae
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Names & Labelling 3D Shapes
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Names of 3D Shapes
Corbett Maths Edges, Faces & Vertices
Online Platforms (with Videos & Exercises)
- Khan Academy
- Names of 3D shapes: Videos & practice
Activities & Resources
- Pixi Maths
- Types of Shapes ppt (Slide 12 Onwards)
- Andy Lutwyche
- Don Steward
- Transum
- Go Teach Maths
- BossMaths
Worksheets
- Dr Austin Maths
- Corbettmaths
- Pixi Maths
- CIMT MEP (online self-checking)
- Miss Konstantine (MathsHKO)
- Kuta Software
- Physics & Maths Tutor
- MME
- Mr Morley Maths
- 3D Shapes: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
Dr Frost Resources
Dr Frost Video
K334: Know the Names of 3D Shapes.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 32a: Recognise cubes, cuboids, pyramids, spheres, and cones. (not yet active)
- 32b: Count the number of faces, edges or vertices of cubes, cuboids, pyramids, spheres, and cones. (not yet active)
- 142a: Recognise and name prisms and cylinders.
- 142b: Understand properties of prisms.
- 32: Exam Practice: Introduction to 3D shapes
- 142: Exam Practice: Properties of prisms and cylinders
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.2 Drawing 3D Shapes with Isometric Paper
Teaching Videos, Exercises & Activities
Tutorial Videos
GCSE Maths – Drawing 3D Shapes Using Isometric Paper – Foundation and Higher by ukmathsteacher
Drawing On Isometric Paper by Minity Maths
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Don Steward
- Transum
- Go Teach Maths
- Dan Walker
- Owen134866
Worksheets
Dr Frost Resources
Dr Frost Videos
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 229a: Draw a shape made of 1 textrmcm3 blocks on isometric paper. (not yet active)
- 229b: Draw cubes and cuboids to scale on isometric paper. (not yet active)
- 229c: Draw triangular prisms on isometric paper. (not yet active)
- 229d: Draw prisms with rectilinear cross-sections on isometric paper. (not yet active)
- 229e: Draw a 3D shape on isometric paper given its net. (not yet active)
- 229: Exam Practice: Draw 3D shapes on isometric paper.
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.3 Viewing Angles: Drawing from a Given Shape
Teaching Videos, Exercises & Activities
Dr Frost Resources
Extension Materials
1.4 Viewing Angles: Drawing Shapes from Given Viewing Angles
Teaching Videos, Exercises & Activities
Tutorial Videos
Plans and Elevations by Maths Genie
GCSE Maths – 2D Projections Of 3D Objects by Cognito
Projections: Plans And Elevations In Maths by Minity Maths
Online Platforms (with Videos & Exercises)
Activities & Resources
- Don Steward
- Transum
- Standards Unit (DfES)
- Standards Unit SS6: Representing 3D Shapes (plans and elevations) (Standards Unit, DfES; PDF
Worksheets
- Corbettmaths
- Views & Elevations Practice Questions (Q7-11) & Solutions
- Pixi Maths
- Maths Genie
- Plans and Elevations: Booklet · Worksheet · Solutions · Lesson · Topic page
- MME
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 229f: Draw a 3D shape on isometric paper, given its plan and elevations. (not yet active)
- 229: Exam Practice: Draw 3D shapes on isometric paper.
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.1 Nets of 3D Shapes
Teaching Videos, Exercises & Activities
Tutorial Videos
Nets Of 3D Shapes Explained by Minity Maths
What's a Net? | Geometry | Math with Mr. J by Math with Mr. J
Identifying 3D shapes and nets by Mr. Dunaway's Math Hacks
Corbett Maths Nets
Online Platforms (with Videos & Exercises)
- Khan Academy
- Nets of 3D shapes: Videos & practice
Activities & Resources
- mathigon is this a net of a cube? Amazing Interactive Resource
- Maths 4 Everyone Exploding Polyhedra Interactive resource
- Andy Lutwyche
- Miss Konstantine (MathsHKO)
- Don Steward
- Transum
- Go Teach Maths
- BossMaths
Worksheets
- Corbettmaths
- Nets Practice Questions & Solutions
- Nets Worksheet & Solutions
- Maths 4 Everyone
Dr Frost Resources
Dr Frost Videos
- Topic Video
- KS 136 Angles in a triangle
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 143a: Identify a 3D shape from its net.
- 143b: Identify a net from a given 3D shape. (not yet active)
- 143c: Determine the number of edges, faces and vertices of a 3D shape given its net.
- 143: Exam Practice: Nets of 3D shapes
Further Practice
- Practise Questions
Extension Materials
Videos & Other Multimedia
Worksheet
3.1 Spheres & Hemispheres
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Surface Area of a Sphere
Corbett Maths Volume of a Sphere
Online Platforms (with Videos & Exercises)
- Khan Academy
- Volume of cylinders, cones & spheres: Videos & practice
Activities & Resources
- Pixi Maths
- Cones, Pyramids and Spheres ppt (Slides 17 Onwards)
- Andy Lutwyche
- Don Steward
- The Chalkface
- Sphere, Cone, Cylinder Volume: Interactive page
- Golden balls✦
- Go Teach Maths
- BossMaths
- BJHarrison1
- Maths Sandpit
Worksheets
- Dr Austin Maths
- Corbettmaths
- Surface Area of a Sphere Practice Questions & Solutions
- Surface Area of a Sphere Worksheet & Solutions
- Volume of a Sphere Practice Questions & Solutions
- Volume of a Sphere Worksheet & Solutions
- Pixi Maths
- Self Marking Sheets by Phil Rhodes
- Volume of prisms, pyramids & spheres (Higher) Excel File
- Surface Area of prisms, pyramids & spheres Excel File
- Maths Genie
- Spheres and Cones: Booklet · Worksheet · Solutions · Lesson · Topic page
- Access Maths
- Cylinders, Spheres & Cones: Surface Area (Fluency & Reasoning) | Volume (Fluency & Reasoning)
- @taylorda01
- MadAsMaths (T. Madas)
- Advanced Mensuration Q1, 3, 7 (difficulty 2–5 of 5)
- Mr Morley Maths
- Surface Area of Sphere, Cone and Pyramid: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
- Pret Homework (@Stacy_Maths)
- Volume of a Sphere (@Stacy_Maths, pptx)
Dr Frost Resources
Dr Frost Video
K657: Find the Volume of a Sphere.
K658: Find the Volume of an Hemisphere.
K659: Find the Radius of a Sphere Given Its Volume.
K660: Find the Surface Area of a Sphere.
K661: Find the Surface Area of an Hemisphere.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 405f: Calculate the volume of a sphere.
- 405g: Determine the radius or diameter of a sphere given its volume.
- 405h: Calculate the volume of a hemisphere.
- 405i: Determine the radius or diameter of a hemisphere given its volume.
- 406k: Calculate the surface area of a sphere.
- 406l: Calculate the surface area of a hemisphere.
- 406m: Determine the radius of a sphere given its surface area.
- 406n: Determine the radius of a hemisphere given its surface area.
- 406o: Determine the surface area of a sphere given its volume, or vice versa.
- 406p: Determine the surface area of a hemisphere or quarter sphere given its volume.
- 405: Exam Practice: Volume of a pyramid, cone or sphere
- 406: Exam Practice: Surface area of a pyramid, cone or sphere/hemisphere
Further Practice
- Practise Questions
Extension Materials
Enrichment Video
3Blue1Brown: But why is a sphere's surface area four times its shadow?
Worksheet
3.2 Pyramids
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Surface Area of a Cone
Corbett Maths Volume of a Pyramid
Corbett Maths Volume of a Cone
Online Platforms (with Videos & Exercises)
- Khan Academy
- Volume of prisms & pyramids: Videos & practice
Activities & Resources
- Pixi Maths
- Cones, Pyramids and Spheres ppt (Slides 1-16)
- Don Steward
- The Chalkface
- Pyramid: PDF · PowerPoint
- Go Teach Maths
- BossMaths
Worksheets
- Dr Austin Maths
- Corbettmaths
- Surface Area of a Cone Practice Questions & Solutions
- Surface Area of a Cone Worksheet & Solutions
- Volume of a Pyramid Practice Questions & Solutions
- Volume of a Pyramid Worksheet & Solutions
- Volume of a Cone Practice Questions & Solutions
- Volume of a Cone Worksheet & Solutions
- Pixi Maths
- Mr Morley Maths
- Volume of Sphere, Cone and Pyramid: Notes jotter/worksheet · Exam questions · Mark scheme
- Pret Homework (@Stacy_Maths)
- Volume of Pyramids and Cones (@Stacy_Maths, pptx)
Dr Frost Resources
Dr Frost Video
K662: Find the Volume of a Pyramid.
K663: Find the Volume of a Cone.
K664: Find the Height of a Cone Given Its Volume.
K665: Find the Radius or Diameter of a Cone Given Its Volume.
K668: Find the Volume of a Frustum of a Cone.
K666: Find the Surface Area of a Cone Given the Perpendicular Height.
K667: Find the Surface Area of a Cone Given the Slanted Height.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 405a: Calculate the volume of a pyramid.
- 405b: Determine an unknown dimension of a pyramid given its volume.
- 405c: Calculate the volume of a cone.
- 405d: Determine the height of a cone given its volume.
- 405e: Determine the radius or diameter of a cone given its volume.
- 405r: Determine the volume of a cone given its net.
- 406a: Calculate the surface area of a square-based pyramid given the side length of the base and the altitude of the lateral face.
- 406b: Calculate the surface area of a square-based pyramid given the side length of the base and the slant height.
- 406c: Calculate the surface area of a square-based pyramid given the side length of the base and the vertical height.
- 406d: Determine the surface area of a cone given the slanted height.
- 406e: Calculate the surface area of a cone given the perpendicular height.
- 406f: Determine the slanted height of a cone given the surface area.
- 406g: Determine the perpendicular height of a cone given the surface area.
- 406h: Determine the surface area of a cone given the volume.
- 406i: Determine the volume of a cone given the surface area.
- 406j: Determine the radius of a cone given the surface area.
- 405: Exam Practice: Volume of a pyramid, cone or sphere
- 406: Exam Practice: Surface area of a pyramid, cone or sphere/hemisphere
Further Practice
- Practise Questions
Extension Materials
Worksheet
3.3 Compound Shapes
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Volume of a Frustum
Online Platforms (with Videos & Exercises)
- Khan Academy
- Volume & surface area word problems: Videos & practice
Activities & Resources
- Andy Lutwyche
- Don Steward
- Transum
- Go Teach Maths
- Mathematics Assessment Project
Worksheets
- Dr Austin Maths
- Corbettmaths
- MME
- Pret Homework (Gemma Down)
- Frustums (Gemma Down, pptx)
Dr Frost Resources
Dr Frost Video
K668: Find the Volume of a Frustum of a Cone.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 405l: Determine the quantity of one solid that makes up the volume of another where at least one has a curved surface.
- 405n: Equate volumes of solids, where at least one has a curved surface, with all but one length known, to determine that length.
- 405o: Equate volumes of solids, where at least one has a curved surface and there is a ratio between two lengths, to determine an unknown.
- 405q: Problem solve involving ratios and volumes of solids, where at least one has a curved surface, to find a length.
- 405s: Determine the volume inside one solid but outside another, where at least one has a curved surface.
- 406q: Determine the surface area of a compound solid with curved faces.
- 406r: Equate the surface area of solids, with all but one length known, to determine that length.
- 407a: Calculate the volume of a compound solid comprising of a cylinder and a cuboid.
- 407b: Calculate the volume of a compound solid comprising of a pyramid and a cuboid.
- 407c: Calculate the volume of a frustum of a cone or pyramid.
- 407d: Calculate the volume of a compound solid comprising of a cone and a hemisphere.
- 407e: Calculate the volume of a compound solid comprising of a cylinder and a hemisphere.
- 407f: Calculate the volume of a compound solid comprising of a cylinder and a cone.
- 407g: Find an unknown dimension in a compound solid where at least one of the parts has a curved surface and the total volume is given.
- 407h: Find an unknown dimension in a frustum given its volume.
- 407i: Determine the volume of a compound solid where the volume of one solid is given.
- 407j: Equate volumes of solids, where one is a frustum, involving algebraic lengths, to obtain an equation for one variable in terms of another.
- 407k: Solve rates of flow problems involving compound curved solids.
- 408a: Calculate the surface area of a compound solid comprising of a cylinder and a cuboid.
- 408b: Calculate the surface area of a compound solid comprising of a semi-cylinder and a cuboid.
- 408c: Calculate the surface area of a compound solid comprising of a pyramid and a cuboid.
- 408d: Calculate the surface area of a compound solid comprising of a cylinder and a cone.
- 408e: Calculate the surface area of a frustum of a pyramid. (not yet active)
- 408f: Calculate the surface area of a frustum of a cone.
- 408g: Calculate the surface area of a compound solid comprising of a cylinder and a hemisphere.
- 408h: Calculate the surface area of a compound solid comprising of a cone and a hemisphere.
- 408i: Determine the surface area of a compound solid where the volume of one solid is given.
- 408j: Determine the surface area of a compound solid given its volume.
- 405: Exam Practice: Volume of a pyramid, cone or sphere
- 406: Exam Practice: Surface area of a pyramid, cone or sphere/hemisphere
- 407: Exam Practice: Volume of more complex compound 3D shapes
- 408: Exam Practice: Surface area of more complex compound 3D shapes
Further Practice
- Practise Questions
Extension Materials
Worksheet
4.1 Working with Formulae
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Dimensional Analysis
Online Platforms (with Videos & Exercises)
Activities & Resources
- Transum
Worksheets
- Corbettmaths
- Dimensional Analysis Practice Questions & Solutions
- Maths 4 Everyone
Dr Frost Resources
Dr Frost Video
K659: Find the Radius of a Sphere Given Its Volume.
K664: Find the Height of a Cone Given Its Volume.
K665: Find the Radius or Diameter of a Cone Given Its Volume.
K666: Find the Surface Area of a Cone Given the Perpendicular Height.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 405d: Determine the height of a cone given its volume.
- 405e: Determine the radius or diameter of a cone given its volume.
- 405g: Determine the radius or diameter of a sphere given its volume.
- 405i: Determine the radius or diameter of a hemisphere given its volume.
- 405j: Determine a density or mass using the volume of a pyramid, cone or sphere.
- 405k: Form and solve equations in one variable where the volume of a pyramid or cone is given.
- 405m: Form an expression for the volume of a pyramid, cone or sphere with algebraic lengths
- 405p: Equate volumes of solids, where at least one has a curved surface, involving algebraic lengths, to obtain an equation for one variable in terms of another.
- 406e: Calculate the surface area of a cone given the perpendicular height.
- 406m: Determine the radius of a sphere given its surface area.
- 406n: Determine the radius of a hemisphere given its surface area.
- 406s: Equate the surface area of solids, involving algebraic lengths, to obtain an equation for one variable in terms of another.
- 405: Exam Practice: Volume of a pyramid, cone or sphere
- 406: Exam Practice: Surface area of a pyramid, cone or sphere/hemisphere
Further Practice
- Practise Questions
Extension Materials
Worksheet
Whole Topic Summary Resources (Including Past Paper Questions)
Download Volume & Surface Area PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Acute Learning Problem Pairs
- Surface area as PowerPoint or PDF
- Volume as PowerPoint or PDF
Worksheets
- Dr Austin Maths
- Maths 4 Everyone
- Andy Lutwyche
- Mathshelper (Jon Stone)
- MathedUp
- Plans, Elevations & Solids: Worksheet · Practice · Quiz · Question Gallery
- Surface Area & Volume: Cones, Spheres & Pyramids: Worksheet · Practice · Quiz · Question Gallery
- Maths Genie
- Surface Area: Booklet · Worksheet · Solutions · Lesson · Topic page
- Kuta Software
- Mathsaurus (Kevin Olding)
- Naiker Maths
- Surface Area: Worksheet
- Physics & Maths Tutor
- MME
- Jo Morgan
- Dr Frost
- UKMaths
- @taylorda01
- Access Maths
- alisongilroy
Activities
- NRICH (student problems)
- Don Steward
- Interactive Maths
- Go Teach Maths
- The Chalkface
- MathsPad
- Dr Austin Maths
- Brilliant
External Whole Topic Past Paper Style Questions
- Transum
- Exam-style questions: Mensuration
- NCETM
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.