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Volume & Surface Area (Edexcel IGCSE Maths A)

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  • What is a vertex on a 3D shape?

    A vertex is a corner of a 3D shape.

    E.g. a square-based pyramid has 5 vertices.

  • What is a face on a 3D shape?

    A face is an individual flat surface of a 3D shape.

    E.g. a cylinder has 2 circular faces (the two 'ends'), along with one curved surface.

  • What is a prism?

    A prism is a 3D shape with the same cross-section throughout.

    E.g. a cuboid is a rectangular prism.

  • True or False?

    A cuboid has six equal, square faces.

    False.

    A cuboid has six rectangular faces.
    They consist of three pairs of equal rectangular faces.

    A cube has six equal, square faces.

  • What does a net of a 3D shape represent?

    A net of a 3D shape is a 2D pattern that could be folded to make that 3D shape.

  • How many edges are there on a square-based pyramid?

    There are eight edges on a square-based pyramid.

  • True or False?

    The base of a tetrahedron is a square.

    False.

    The base of a tetrahedron is a triangle.

  • What shape is the cross-section of a cylinder?

    The cross-section of a cylinder is a circle.

  • True or False?

    A triangular prism has two equal triangular faces and three rectangular faces.

    True.

    A triangular prism has two equal triangular faces and three rectangular faces.

  • True or False?

    A cube is a type of prism.

    True.

    A cube is a type of prism with a square cross-section.

  • What is the formula for the volume of a cuboid?

    The formula for the volume of a cuboid is V equals l cross times w cross times h

    Where:

    • V equalsvolume

    • l equalslength

    • w equalswidth

    • h equalsheight

  • What is the formula for the volume of a cylinder?

    The formula for the volume of a cylinder is V equals pi r squared h

    Where:

    • V equalsvolume

    • r equalsradius

    • h equalsheight

  • What is the formula for the volume of a cone?

    The formula for the volume of a cone is V equals 1 third pi r squared h

    Where:

    • V equalsvolume

    • r equalsradius

    • h equalsperpendicular height

  • What is the formula for the volume of a sphere?

    The formula for the volume of a sphere is V equals 4 over 3 pi r cubed

    Where:

    • V equalsvolume

    • r equalsradius

  • What is the formula for the volume of a prism?

    The formula for the volume of a prism is V equals A l

    Where:

    • V equalsvolume

    • A equalscross-sectional area

    • l equalslength

  • What is a frustum?

    A frustum is a truncated (chopped-off) cone.

    E.g.

    A truncated cone (frustum).

  • How can the volume of a hemisphere be found?

    The volume of a hemisphere can be found by halving the volume of the complete sphere.

  • How can the volume of a frustum be found?

    The volume of a frustum is the volume of the larger cone minus the volume of the smaller cone that has been 'cut off'.

  • What is the formula for the surface area of a cylinder?

    The formula for the surface area of a cylinder is A equals 2 pi r squared plus 2 pi r h

    Where:

    • A equals surface area

    • r equalsradius

    • h equalsheight

  • True or False?

    The formula for the curved surface area of a cone is A equals pi r l plus pi r squared

    Where:

    • A equalssurface area

    • r equalsradius

    • l equalsslant height

    False.

    A equals pi r l plus pi r squared is the total surface area of a cone.

    The formula for the curved surface area of a cone is A equals pi r l

    Where:

    • A equalssurface area

    • r equalsradius

    • l equalsslant height

    (pi r squared is the area of the circular base of the cone.)

  • What is the formula for the surface area of a sphere?

    The formula for the surface area of a sphere is A equals 4 pi r squared

    Where:

    • A equalssurface area

    • r equalsradius

  • True or False?

    The surface area of a hemisphere comprises the surface area of a sphere and the area of a circle of the same radius.

    False.

    The surface area of a hemisphere comprises half the surface area of a sphere, and the area of a circle of the same radius.

  • True or False?

    The surface area of a cuboid consists of three pairs of equal rectangles.

    True.

    The surface area of a cuboid consists of three pairs of equal rectangles.

  • What is the formula for the total surface area of a cone?

    The formula for the total surface area of a cone is A equals pi r squared plus pi r l

    Where:

    • A equalssurface area

    • r equalsradius

    • l equalsslant height

  • True or False?

    The net of a cylinder consists of two circles and a rectangle.

    True.

    The net of a cylinder consists of two circles and a rectangle.

Previous:Circles, Arcs & SectorsNext:Congruence, Similarity & Geometrical Proof

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions

    6. Topic 6

      Percentages

    7. Topic 7

      Compound Interest & Depreciation

    8. Topic 8

      Fractions, Decimals & Percentages

    9. Topic 9

      Rounding, Estimation & Bounds

    10. Topic 10

      Surds

    11. Topic 11

      Using a Calculator

    12. Topic 12

      Ratio Toolkit

    13. Topic 13

      Ratio Problem Solving

    14. Topic 14

      Exchange Rates & Best Buys

    15. Topic 15

      Direct & Inverse Proportion

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Solving Linear Equations

    10. Topic 10

      Solving Quadratic Equations

    11. Topic 11

      Solving Inequalities

    12. Topic 12

      Simultaneous Equations

    13. Topic 13

      Forming & Solving Equations

    1. Topic 1

      Sequences

    2. Topic 2

      Functions

    3. Topic 3

      Coordinate Geometry

    4. Topic 4

      Linear Graphs y = mx + c

    5. Topic 5

      Graphs of Functions

    6. Topic 6

      Estimating Gradients

    7. Topic 7

      Real-Life Graphs

    8. Topic 8

      Graphing Inequalities

    9. Topic 9

      Transformations of Graphs

    10. Topic 10

      Differentiation

    1. Topic 1

      Standard & Compound Units

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing & Constructions

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Right-Angled Triangles - Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Statistics Toolkit

    2. Topic 2

      Histograms

    3. Topic 3

      Cumulative Frequency Diagrams

    4. Topic 4

      Probability Toolkit

    5. Topic 5

      Probability Diagrams - Venn & Tree Diagrams

    6. Topic 6

      Combined & Conditional Probability