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3. Trigonometric Ratios & Geometric Equations
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Geometry

3.18 Arc length and sector area

Lesson
Practice

Interactive practice questions

If the circumference of the circle is equal to $144$144 cm, find the length of the solid arc.

A circle is depicted with its arc and two radii outlined with a solid green line, thus forming a sector, while the rest of the circle is represented with a dashed green line. The two radii of the sector, formed a central angle labeled as 160 degrees.
Easy
1min

The diagram shows a sector of a circle of radius $4$4 units, formed from an angle of size $180^\circ$180°.

Find the exact length of the arc. Do not round your answer.

Easy
2min

The diagram shows a sector of a circle of radius $4$4 units, formed from an angle of size $135^\circ$135°.

Find the length of the arc rounded to two decimal places.

Easy
2min

The diagram shows a sector of a circle of radius $6$6 units, formed from an angle of size $290^\circ$290°.

Find the exact length of the arc.

Easy
3min
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Outcomes

G.CO.A.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G.C.B.5

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

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