An arc is a fraction of the way round a circle, so its length is that same fraction of the circumference. These free printable worksheets keep to the curved edge alone.
The step from a whole circle to a piece of one is a single multiplication, and it is the step a formula sheet hides. The circumference is 2πr; the arc is that times the angle over 360. A child who writes the fraction down first — 90 over 360, which is a quarter — has usually finished before one who reaches for the formula.
Why this sheet works
Every angle here divides 360 exactly, and the radii are chosen so the answer lands on two decimal places. So the paper never says round to the nearest tenth and the key can be used to check rather than to compare. π is 3.14 throughout.
How this one works
One question from this sheet, worked through a step at a time.
Arc: 135° of a circle, radius 12
135/360=3/8
2 × 3.14 × 12=75.36
3/8of75.36=28.26
28.26 cm
A slice is a FRACTION of the whole circle, and the angle says which fraction. A full turn is 360°, so 135° is 135 out of 360 — that is 3/8 of the circle. Write that down before touching a formula.
Now the whole circle, as if there were no slice. All the way round is 2 × π × r: 2 × 3.14 × 12 = 75.36 cm.
Then take the slice's share of it: 3/8 of 75.36 is 28.26.
So the curved edge is 28.26 cm. Check the unit against what was asked — a curved edge is a length and a slice is an area, and getting cm where you expected the other one means you answered the other question.
