Four Parts
The circle of radius 4cm is divided into four congruent parts by arcs of radius 2cm as shown. What is the length of the perimeter of one of the parts, in cm?
Age
14 to 16
Challenge level
Problem
Image
What is the length of the perimeter of one of the parts, in cm?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
The circumference of a circle with radius $r$ is $2 \pi r$.
Each piece has a quarter of the circle with radius $4$ together with two semicircular arcs of radius $2$.
The arc of the large circle has length $\frac{1}{4} \times 2 \times \pi \times 4 = 2 \pi$.
The semicircular arcs have length $\frac{1}{2} \times 2 \times \pi \times 2 = 2 \pi$.
Therefore the overall perimeter is $3 \times 2\pi = 6\pi$.