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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 3 — 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

$7\pi$ cm

$14$ cm

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

10 cm

5 cm

$10\pi$ cm

$5\pi$ cm

A sector of a circle has an area of $A = 50\pi$ cm $^{2}$ and an angle of $120^\circ$ . What is the radius of the circle?

10 cm

5 cm

15 cm

20 cm

What is the length of an arc in a circle of radius $r = 4$ m that subtends an angle of $90^\circ$ ?

$2\pi$ m

$4\pi$ m

$\frac{4\pi}{2}$ m

$4$ m

A circle has a diameter of $d = 12$ cm. What is the area of the circle?

$36\pi$ cm $^{2}$

$12\pi$ cm $^{2}$

$144\pi$ cm $^{2}$

$48\pi$ cm $^{2}$

If the radius of a circle is increased from $r = 3$ m to $r = 6$ m, by what factor does the circumference increase?

1.5

A sector of a circle with radius $r = 5$ cm has an angle of $150^\circ$ . What is the area of the sector?

$\frac{25\pi}{3}$ cm $^{2}$

$\frac{15\pi}{2}$ cm $^{2}$

$\frac{5\pi}{2}$ cm $^{2}$

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

A circle's radius is $4$ cm. If an arc length is $8$ cm, what is the angle in degrees subtended by this arc at the center of the circle?

180^\circ

360^\circ

90^\circ

120^\circ

A circular park has a circumference of $C = 40\pi$ m. What is the area of the park?

$100\pi$ m $^{2}$

$160\pi$ m $^{2}$

$200\pi$ m $^{2}$

$80\pi$ m $^{2}$

10.

What is the total angle in degrees of all arcs in a full circle?

360^\circ

180^\circ

90^\circ

720^\circ

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