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

NameDate

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

Jun paints a curved stripe along the rim of a round clock. Circle O has diameter 12 cm, and ∠COD = 150°. How long is arc CD in cm, in terms of π?
Luz draws a curved line along the edge of a round plate. Circle O has diameter 16 cm, and ∠COD = 45°. How long is arc CD in cm, in terms of π?
Milo walks along the curved edge of a round pond in the park. Circle O has diameter 30 m, and ∠COD = 84°. How long is arc CD in meters, in terms of π?
Noah orders a round pizza and eats one wedge. Circle O has diameter 8 in.; sector COD has a 135° angle. What is its area in square inches, in terms of π?
Pia sews one wedge of a round rug in a new color. Circle O has diameter 12 in.; sector COD has a 100° angle. What is its area in square inches, in terms of π?
Ren cuts a thin wedge from a round cake. Circle O has diameter 18 in.; sector COD has a 40° angle. What is its area in square inches, in terms of π?
Tala plants flowers in one wedge of a round flower bed. Circle O has diameter 24 ft; sector COD has a 50° angle. What is its area in square feet, in terms of π?
Zee jogs a curved path by a round pond: a 50° arc of a circle with radius 7 meters. Using 3.14 for π, how long is the path in meters, to the nearest tenth?
Ari rides a curved bike path: a 70° arc of a circle with radius 12 feet. Using 3.14 for π, how long is the path in feet, to the nearest tenth?
Bo paints a curved line on a round clock: a 110° arc of a circle with radius 9 cm. Using 3.14 for π, how long is the path in cm, to the nearest tenth?

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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