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Volume (Edexcel IGCSE Maths A): Revision Note

Exam code: 4MA1

Naomi C

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Naomi C

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Volume

What is volume?

  • The volume of a 3D shape is a measure of how much space it takes up

  • You need to be able to calculate the volumes of a number of common 3D shapes, including:

    • Cubes and cuboids

    • Prisms

    • Pyramids

    • Cylinders

    • Spheres

How do I find the volume of a cube or a cuboid?

  • A cube is a special cuboid, where the length, width and height are all of equal length

  • A cuboid is another name for a rectangular-based prism

  • To find the volume, V, of a cube or a cuboid, with length, l, width, w, and height, h, use the formula

    • V equals l w h

    • This formula is not given to you in the exam

Volume of a cuboid

  • You will sometimes see the terms  'depth' or 'breadth' instead of 'height' or 'width'

How do I find the volume of a prism?

  • A prism is a 3D object with a constant cross-sectional area

  • To find the volume, V, of a prism, with cross-sectional area, A, and length, l, use the formula

    • V equals A l

    • This formula is not given to you in the exam

Volume of a prism

  • Note that the cross-section can be any shape, so as long as you know its area and the length of the prism, you can calculate its volume

    • If you know the volume and length of the prism, you can calculate the area of the cross-section

How do I find the volume of a cylinder?

  • To calculate the volume, V, of a cylinder with radius, r, and height, h, use the formula

    • V equals pi italic space r squared h

    • This formula is not given to you in the exam

Volume of a cylinder

  • Note that a cylinder is similar to a prism, its cross-section is a circle with area pi italic space r squared, and its length is h

How do I find the volume of a pyramid?

  • To calculate the volume, V, of a pyramid with base area, A, and perpendicular height, h, use the formula

    • V equals 1 third A h

    • This formula is given to you in the exam

Volume of a pyramid

  • The height must be a line from the top of the pyramid that is perpendicular to the base

  • The base of a pyramid could be a square, a rectangle or a triangle

How do I find the volume of a cone?

  • To calculate the volume, V, of a cone with base radius, r, and perpendicular height, h, use the formula

    • V equals 1 third pi italic space r to the power of italic 2 h

    • This formula is given to you in the exam

Cone volume, IGCSE & GCSE Maths revision notes

  • Note that volume formula for a cone is similar to a pyramid

  • The height must be a line from the top of the cone that is perpendicular to the base

How do I find the volume of a sphere?

  • To calculate the volume, V, of a sphere with radius, r, use the formula

    • V equals 4 over 3 pi italic space r cubed

    • This formula is given to you in the exam

Sphere Radius r, IGCSE & GCSE Maths revision notes

Examiner Tips and Tricks

  • You only need to memorise the volume formulae for:

    • Cuboids: V equals l w h

    • Prisms: V equals A l

    • Cylinders: V equals pi italic space r squared h

Worked Example

A cylinder is shown.

Cylinder

The radius, r, is 8 cm and the height, h, is 20 cm.

Calculate the volume of the cylinder, giving your answer correct to 3 significant figures.
 

A cylinder is similar to a prism but with a circular base
The volume of any prism, V, is its base area × height, h, where the base area here is for a circle, pi italic space r squared
 

V equals pi space r squared h
 

Substitute r  = 8 and h  = 20 into the formula
 

V equals straight pi cross times 8 squared cross times 20
 

Work out this value on a calculator
 

4021.238...
 

Round the answer to 3 significant figures

4020 cm3

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Naomi C

Author: Naomi C

Expertise: Maths Content Creator

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

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