Grade 10 · Math · Geometry

10th grade Arc length and the area of a sector worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Arc length and the area of a sector

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Jun measures the crust of one slice of a round pizza. Circle O has radius 6 cm, and ∠COD = 60°. How long is arc CD in cm, in terms of π?
Kira paints a curved stripe along the edge of a round clock face. Circle O has radius 9 cm, and ∠COD = 120°. How long is arc CD in cm, in terms of π?
Luz pipes icing along part of the edge of a round cookie. Circle O has radius 4 cm, and ∠COD = 135°. How long is arc CD in cm, in terms of π?
Milo glues ribbon along part of the rim of a drum. Circle O has radius 10 cm, and ∠COD = 72°. How long is arc CD in cm, in terms of π?
Pia covers one wedge of a round plate with a sticker. Circle O has radius 3 in.; sector COD has a 120° angle. What is its area in square inches, in terms of π?
Ren paints one thin wedge on a round rug. Circle O has radius 8 in.; sector COD has a 45° angle. What is its area in square inches, in terms of π?
Tala frosts the top of one wedge of a round cake. Circle O has radius 10 in.; sector COD has a 36° angle. What is its area in square inches, in terms of π?
Zee takes a thin slice of a round pizza. Sector COD of circle O has a 40° angle. What fraction of the circle's area is sector COD?
Bo cuts one wedge from a round cake. Sector COD of circle O has a 75° angle. What fraction of the circle's area is sector COD?
Esme shades a clock face from 12 all the way round to 9. Sector COD of circle O has a 270° angle. What fraction of the circle's area is sector COD?

10th grade Arc length and the area of a sector worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Arc length and the area of a sector. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the length of an arc as a fraction of the distance around.
I can find the area of a sector as a fraction of the circle's area.
I can work back to the radius or the angle from an arc length or a sector area.

Standard: G-C.B.5

Words to know

arc length: How far it is along the edge of the circle, from one end of the arc to the other.

sector: A pizza-slice part of a circle between two radii.

circumference: The distance around a circle: 2 × π × radius.

area of a circle: π × radius × radius.

in terms of π: Keep π as a letter in the answer, like 6π.

fraction of the turn: The angle ÷ 360.

Common mistakes

Your child used the area of the circle when the question asked for a length along the edge.

Your child used π × radius for the distance around a circle, which is half of it.

Your child gave the arc's angle in degrees when the question asked for its length.

What to say

Ask: is the arc a distance or a space to cover?

Ask: how many radii fit across a circle?

Ask: is the answer a turn or a distance?

Questions parents ask

What is the most common mistake with arc length and the area of a sector?

Your child used the area of the circle when the question asked for a length along the edge.

How can I help my child with arc length and the area of a sector?

Ask: is the arc a distance or a space to cover?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

See all Geometry

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records