Volume (Edexcel IGCSE Maths)

Spec point — 4.10F

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
  • Cylinders
  • Spheres
  • Cones

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

  • $V=lwh$
  • This formula is not given to you in the exam

• 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

  • $V=Al$
  • This formula is given to you in the exam

• 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

  • $V=πr^{2}h$
  • This formula is given to you in the exam

• Note that a cylinder is similar to a prism, its cross-section is a circle with area $πr^{2}$, and its length is h

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

  • $V=\frac{1}{3}πr^{2}h$
  • This formula is given to you in the exam

• 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

  • $V=\frac{4}{3}πr^{3}$
  • This formula is given to you in your exam

Exam Hint You only need to memorise the volume formulae for cuboids!

Worked Example A cylinder is shown.

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.

Answer:

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, *$πr^{2}$

$V=πr^{2}h$

Substitute r = 8 and h = 20 into the formula

$V=π\times8^{2}\times20$

Work out this value on a calculator

4021.238...

Round the answer to 3 significant figures

Final answer: 4020 cm³