Skip to Main Content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.
Library name header

Mathematics

Problem Solving

Mathematics is full of problems that need to be solved. A problem may be about solving an equation, calculating an amount of something, finding an answer to a word problem, etc. You can use problem-solving strategies to help you work out the correct answer for mathematics problems in your assignments. See the steps below:

 

Steps for Mathematics Problem Solving

1. Read the question carefully to the end

Example:
Find the volume of fluid which can be contained inside a 2.1 m length of cylindrical pipe with diameter 120mm. The walls of the pipe are 2 mm thick.  Write your answer in cubic metres. Round your final answer to 3 decimal places.

2. Identify the question itself (underline or highlight what you are being asked to find)

Find the volume of fluid which can be contained inside a 2.1 m length of cylindrical pipe with diameter 120mm. The walls of the pipe are 2 mm thick. Write your answer in cubic metres. Round your final answer to 3 decimal places.

3. Write down any data you have been given including units

Pipe length = 2.1m

Pipe diameter = 120mm
Thickness of pipe = 2mm

4. Identify and write down any formulae or relationships which may apply to the situation

Volume of a cylinder
Vol=πr^2L where r = radius, L=length

5. Draw a diagram of the situation or write down the steps required to solve the problem

pipe wall diagram

6. Convert any given data to units required in the final answer

length = 2.1m
diameter = 120mm = 120÷1000 = 0.12m
thickness = 2mm = 2÷1000 = 0.002m
radius = diameter÷2 = 0.12÷2 = 0.06m

7. Check if you have used all the information/data given

length, diameter, thickness

8. Communicate your working clearly (use words to describe your working if necessary)

"How do I use wall of pipe measurement? The question asks for volume of fluid inside the pipe. Therefore the internal pipe radius is needed in the calculation i.e. the pipe radius minus the width of the wall of the pipe."
60mm - 2mm = 58mm = 0.058m (internal radius in m)

Vol = πr^2L = π × 0.058^2 × 2.1
Vol = 0.022m^3 (3 decimal points)

9. Check your final answer

•    Does it make physical or logical sense?
•    Did you answer the question asked?
•    Did you answer all parts of the question?
•    Is your answer in the correct units?
•    Is your answer rounded to the required decimal places or significant figures?