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Arc and Circumference

This worksheet covers Arc and Circumference, which is part of the Circles Destroyer module in the SAT Math Destroyer Crash Course course. Practice problems are designed to strengthen key concepts and build confidence.

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Arc and Circumference

Circles Destroyer • SAT Math Destroyer Crash Course

Set 2 — Mastery

A circle has a radius of $r = 7$ units. What is the length of an arc that subtends an angle of $60^{ ext{o}}$ at the center of the circle?

$\frac{7}{3}$

$7$

$\frac{7\pi}{3}$

$\frac{14\pi}{3}$

If the circumference of a circle is $C = 20\pi$ units, what is the radius of the circle?

$10$

$5$

$\frac{20}{\pi}$

$\frac{10}{\pi}$

A circular track has a diameter of $d = 12$ meters. What is the length of the track?

$6\pi$

$12\pi$

$24$

$36$

Find the area of a sector formed by a $90^{\text{o}}$ angle in a circle with radius $r = 4$ units.

$8$

$4\pi$

$8\pi$

$2\pi$

A circle has a circumference of $C = 15\pi$ units. If a point on the circle moves through an arc length of $5\pi$ units, what fraction of the circle's circumference has the point traveled?

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{1}{4}$

What is the angle in degrees of a sector of a circle with a radius of $r = 10$ units that has an area of $A = 25\pi$ square units?

$45$

$90$

$60$

$30$

A circle has a radius of $r = 8$ units. If a central angle measures $120^{\text{o}}$ , what is the arc length?

$\frac{8\pi}{3}$

$\frac{16\pi}{3}$

$\frac{4\pi}{3}$

$8\pi$

A wheel has a radius of $r = 3$ feet. How far does a point on its edge travel when the wheel makes one complete revolution?

$6\pi$

$9\pi$

$3\pi$

$12\pi$

If the area of a circle is $A = 25\pi$ square units, what is the radius of the circle?

$5$

$10$

$25$

$12.5$

10.

A circular garden has a radius of $r = 6$ meters. What is the area of the garden?

$12\pi$

$36\pi$

$18\pi$

$24\pi$

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