Grade 10 · Math · Geometry

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

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Arc length and the area of a sector

Grade 10 Math Worksheet - Challenge Me

NameDate

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

Jun measures the crust of a pizza slice. Arc CD of circle O is 4π cm long, and ∠COD = 60°. What is the radius of circle O, in cm?
Kira measures a curved stripe on a round clock. Arc CD of circle O is 5π cm long, and ∠COD = 150°. What is the radius of circle O, in cm?
Luz measures trim along part of a drum's rim. Arc CD of circle O is 6π cm long, and ∠COD = 54°. What is the radius of circle O, in cm?
Milo measures icing along a cookie's edge. Arc CD of circle O is 9π cm long, and ∠COD = 162°. What is the radius of circle O, in cm?
Noah sews one wedge of a round rug. Circle O has radius 6 in., and sector COD has area 10π square inches. What is the measure of ∠COD, in degrees?
Ren mows one wedge of a round lawn. Circle O has radius 10 m, and sector COD has area 20π square meters. What is the measure of ∠COD, in degrees?
Tala frosts most of the top of a small round cake. Circle O has radius 3 in., and sector COD has area 6π square inches. What is the measure of ∠COD, in degrees?
Ari edges a rug wedge with ribbon. Circle O has radius 10 cm; arc CD is 3π cm long. What is the area of sector COD in square cm, in terms of π?
Bo cuts a wedge of a round cake. Circle O has radius 9 cm; arc CD is 5π cm long. What is the area of sector COD in square cm, in terms of π?
Esme paints one wedge of a round plate. Circle O has radius 8 cm; arc CD is 2π cm long. What is the area of sector COD in square cm, in terms of π?

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

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