Volume (CIE IGCSE Maths: Core)

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
  • 
  • 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
  • 
  • 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
  • 
  • 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 , 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
  • 
  • This formula is given to you in the exam

• • 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
  • 
  • This formula is given to you in the exam

• • 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
  • 
  • This formula is given to in your exam

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