A slice of a circle is a fraction of the whole one, and once that fraction is named the rest is arithmetic already known. These free printable worksheets ask for the curved edge or the area of a sector, with the angle drawn on the figure.
A 90° slice is a quarter of the circle, so its curved edge is a quarter of the circumference and its area is a quarter of the area. Writing the fraction down first — 90 over 360, which is one quarter — turns both questions into one multiplication and removes any need to remember two separate formulas.
Why this sheet works
The two questions are mixed on purpose. Arc length uses 2πr and sector area uses πr², and a page of only one kind lets a child pick the formula by habit rather than by reading. Which is being asked for is stated beside each figure, and the units are the giveaway: a length is in cm, an area in cm².
How this one works
One question from this sheet, worked through a step at a time.
Arc: 90° of a circle, radius 7
90/360=1/4
2 × 3.14 × 7=43.96
1/4of43.96=10.99
10.99 cm
A slice is a FRACTION of the whole circle, and the angle says which fraction. A full turn is 360°, so 90° is 90 out of 360 — that is 1/4 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 × 7 = 43.96 cm.
Then take the slice's share of it: 1/4 of 43.96 is 10.99.
So the curved edge is 10.99 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.
