Level 2 · Ages 8–11
Read it again any time, including while you work through the exercises.
You already know how to measure around a square or a rectangle: you add the sides. But how do you measure around a circle, which has no straight side at all? Imagine wrapping a string around a round box, then unrolling the string to measure it: that length is the perimeter of the circle, also called the circumference.
Mathematicians discovered an amazing secret: if you divide the distance around a circle by its diameter (the line crossing the circle through the centre), you always get the same number, whatever the circle! This number is called pi, written π, and it is about 3.14.
This gives a very simple formula: P = π × d. The distance around a circle is about 3.14 times its diameter. And since the diameter is twice the radius (d = 2 × r), you can also write P = 2 × π × r.
Watch out for the classic trap: if the problem gives you the radius, remember to double it to get the diameter before multiplying by π. Always check: radius or diameter?
In this course we take π ≈ 3.14 for every calculation. Now go all the way around!
A circle has a diameter of 10 cm. Find its perimeter (take π ≈ 3.14).
P = π × d
I write the circle perimeter formula: pi times the diameter.
P ≈ 3,14 × 10
I replace π with 3.14 and d with 10 cm.
P ≈ 31,4
Multiplying by 10 shifts the decimal point one place to the right.
Result: The perimeter of the circle is about 31.4 cm.
A circle has a radius of 3 cm. Find its perimeter (take π ≈ 3.14).
d = 2 × 3 = 6
Careful, I am given the radius! I double it first to get the diameter: 6 cm.
P ≈ 3,14 × 6
I apply the formula P = π × d with the diameter I found.
P ≈ 18,84
3.14 × 6 = 18.84: I check with 3 × 6 = 18, my result is just above, that makes sense.
Result: The perimeter of the circle is about 18.84 cm.