Problem Solving with Volumes

Problem Solving with Volumes

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

  • A frustum is a truncated (chopped-off) cone or pyramid

    • The volume of a frustum will be the volume of the smaller cone or pyramid subtracted from the volume of the larger cone or pyramid

• 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