Problem-Solving-With-Volumes Edexcel Higher

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Exam code:1MA1

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.

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.

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

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Maths Gcse Edexcel Higher

Problem-Solving-With-Volumes Edexcel Higher