Skip to main content
Links to the University of Cambridge website
Links to the NRICH website Home page
Nurturing young mathematicians: teacher webinars
30 April (Primary)
,
1 May (Secondary)
menu
search
Teachers
expand_more
Early years
Primary
Secondary
Post-16
Events
Professional development
Students
expand_more
Primary
Secondary
Post-16
Parents
expand_more
Early Years
Primary
Secondary
Post-16
Problem-solving Schools
About NRICH
expand_more
About us
Impact stories
Support us
Our funders
Contact us
search
Site search
search
Or search by topic
Number and algebra
The Number System and Place Value
Calculations and Numerical Methods
Fractions, Decimals, Percentages, Ratio and Proportion
Properties of Numbers
Patterns, Sequences and Structure
Algebraic expressions, equations and formulae
Coordinates, Functions and Graphs
Geometry and measure
Angles, Polygons, and Geometrical Proof
3D Geometry, Shape and Space
Measuring and calculating with units
Transformations and constructions
Pythagoras and Trigonometry
Vectors and Matrices
Probability and statistics
Handling, Processing and Representing Data
Probability
Working mathematically
Thinking mathematically
Mathematical mindsets
For younger learners
Early Years Foundation Stage
Advanced mathematics
Decision Mathematics and Combinatorics
Advanced Probability and Statistics
Mechanics
Calculus
Running Race
Age
14 to 16
Short
Challenge Level
Secondary curriculum
Problem
Getting Started
Solutions
Imagine a circle of diameter $1$ unit, and another circle of a similar diameter, and another.
What is the total perimeter of these three circles (you can leave your answer with $\pi$ in it)?
What is the perimeter of a circle of diameter $3$ units?
*****
Now imagine two circles - one of diameter $2$ units and one of diameter $3$ units.
What is the total perimeter of these two circles?
What is the perimeter of a circle of diameter 5units?
*****
What do you notice?
Is this generally the case with combinations of circles whose total diameters are equal?
Can you explain why?
This problem is taken from the
UKMT Mathematical Challenges
.
You can find more short problems, arranged by curriculum topic, in our
short problems collection
.