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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 1 — Mastery

A circle has a radius of $r = 7$ cm. What is the length of an arc that subtends an angle of $60^\circ$ at the center of the circle?

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

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

$\frac{7\pi}{6}$ cm

$\frac{14\pi}{6}$ cm

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

5 cm

10 cm

15 cm

20 cm

A sector of a circle has an area of $A = 15\pi$ cm $^{2}$ and subtends an angle of $120^\circ$ . What is the radius of the circle?

5 cm

10 cm

15 cm

20 cm

What is the length of a circle's circumference if its diameter is $d = 14$ cm?

$14\pi$ cm

$28\pi$ cm

$7\pi$ cm

$21\pi$ cm

A circular garden has a radius of $r = 12$ m. How long is the arc of the garden that corresponds to a central angle of $90^\circ$ ?

$6\pi$ m

$12\pi$ m

$3\pi$ m

$9\pi$ m

The radius of a circular track is $r = 10$ m. What is the area of the sector formed by a $45^\circ$ angle at the center?

$\frac{25\pi}{2}$ m $^{2}$

$25\pi$ m $^{2}$

$5\pi$ m $^{2}$

$20\pi$ m $^{2}$

If a circle has an arc length of $8\pi$ cm and a radius of $r = 8$ cm, what is the central angle $\theta$ in degrees?

180^\circ

120^\circ

90^\circ

360^\circ

A wheel has a radius of $r = 5$ inches. If it makes one complete revolution, what is the distance it covers?

$5\pi$ inches

$10\pi$ inches

$20\pi$ inches

$25\pi$ inches

A circular pizza has a diameter of $d = 16$ inches. How much pizza is there if a slice with an angle of $30^\circ$ is taken out?

$\frac{64\pi}{3}$ in $^{2}$

$\frac{32\pi}{3}$ in $^{2}$

$\frac{16\pi}{3}$ in $^{2}$

$\frac{24\pi}{3}$ in $^{2}$

10.

What is the radius of a circle whose arc length is $5\pi$ cm and subtends an angle of $60^\circ$ ?

5 cm

10 cm

15 cm

20 cm

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