4.9.4

Volume of 3D Shapes

Test yourself

Volume of 3D Shapes

We can use formulae to calculate the volume of common shapes.

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Prism

  • Volume = area of base × length.
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Cuboid

  • Remember that a cuboid is a prism with rectangular base.
    • Volume = width × height × length = area of base × length.
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Cylinder

  • The area of a circle is πr2 so:
    • V = πr2 × h
  • Where h is the height of the cylinder.

Volume of 3D Shapes

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Sphere

  • The volume of a sphere is:
    • V = 43πr3
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Hemisphere

  • A hemisphere is half a sphere, so its volume is half that of a sphere:
    • V = 23πr3
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Cone

  • The volume of a cone is V = 13πr2h
  • Where h is the vertical height of the cone (not the slant height).
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Pyramid

  • The volume of a pyramid is V = 13 × base area × vertical height.
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Frustum

  • A frustum of a cone is a cone with its top removed.
  • The part that is removed is also a cone so the volume is:
    • V = V(whole cone) - V(removed cone)

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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