Problem Solving with Volumes (Edexcel GCSE Maths) : Revision Note

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

Examiner Tips and Tricks

  • 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 diagram shows a prism.

L-shaped prism diagram

Work out the volume of the prism.

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

Worked Example

The diagram shows a truncated cone (a frustum).
Using the given dimensions, find the volume of the frustum to 3 significant figures.

3-7-1-problem-solving-with-volume-2

To find the volume of the frustum, find the volume of the larger cone (30 cm tall, with a radius of 20 cm), and subtract the volume of the smaller cone (15 cm tall, with a radius of 10 cm)

Formula for the volume of a cone: 1 third pi space r squared straight h

Calculate the volume of the larger cone

V subscript L equals 1 third cross times pi cross times 20 squared cross times 30 equals 4000 pi equals 12 space 566.37061... space cm cubed

Calculate the volume of the smaller cone

straight V subscript straight S equals 1 third cross times pi cross times 10 squared cross times 15 equals 500 pi equals 1 space 570.796327... space cm cubed

Find the difference

V subscript L minus V subscript S equals 4000 pi minus 500 pi equals 3500 pi equals 10 space 995.57429... space cm cubed

Round to 3 significant figures 

11 000 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.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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