Volume (Edexcel GCSE Maths: Foundation)

Revision Note

Test yourself
Naomi C

Author

Naomi C

Last updated

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?

  • 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 Tip

  • 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 = 8 and = 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

Problem Solving with Volumes

What is problem solving?

  • Problem solving, usually has two key features:
    • A question is given as a real-life scenario
      • eg. The volume of water in a swimming pool...
    • There is usually more than one topic of maths you will need in order to answer the question
      • eg. Volume and money

What are common problems that involve volume?

  • Volume is a commonly used topic of 'real-world' maths
    • For example, a carton of juice in the shape of a cuboid, a cylindrical tin and a triangular prism chocolate box all involve volume
  • Typically, the 'real-world' scenarios also have a cost
    • A lot of volume problems also involve calculations with money

How do I solve problems involving volume?

  • Often the 3D object in a question will not be a standard cuboid, cone, sphere, etc.
    • It will likely either be:
      • A prism (3D shape with the same cross-section running through it)
      • A portion or fraction of a standard shape (a hemisphere for example)
      • A compound object (an object made up of two or more standard 3D objects)
  • If the object is a prism, recall that the volume of a prism is the cross-sectional area × its length
    • The cross-sectional area may be a compound 2D shape
      • For example, an L-shape, or a combination of a rectangle and a triangle 
  • If the object is a fraction of a standard shape, consider the "full" version of the object and find the appropriate fraction of it
    • A hemisphere is half a sphere
  • If the object is a compound object, find the volumes of the individual standard 3D objects and add them together
  • Problem solving questions could appear on either a non-calculator paper or a calculator paper

Examiner Tip

  • Before you start calculating, make a quick note of your plan to tackle the question
    • For example, "Find the area of the triangle and the rectangle, add together, multiply by the length"

Worked example

The volume is the area of the cross section × length (10 cm)
Find the area by splitting into a 7 × 4 and a (9 - 4) × 2 rectangle (or a 9 × 2 and a (7 - 2) × 4 rectangle) 
 

 7 × 4 + (9 - 4) × 2 = 38 cm2
 

Find the volume (by multiplying 38 by 10)
 

38 × 10

380 cm3

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Naomi C

Author: Naomi C

Expertise: Maths

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.