Arc Length and Radians: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

Find the length of the selected $105^\circ$ arc in a circle of radius $16$ cm.

Answer choices for question 1 A $\tfrac{14\pi}{3}$ cm B $\tfrac{56\pi}{3}$ cm C $\tfrac{28\pi}{3}$ cm D $28\pi$ cm
2

A selected arc is $18\pi$ cm long and has central turn $\tfrac{3\pi}{4}$ radians. Find the circle's radius.

Answer choices for question 2 A $24$ cm B $12$ cm C $\tfrac{27\pi^2}{2}$ cm D $\tfrac1{24}$ cm
3

A circle has radius $15$ cm. The minor central angle between $OA$ and $OB$ is $132^\circ$ . Find the length of the major arc with endpoints $A$ and $B$ .

Answer choices for question 3 A $11\pi$ cm B $38\pi$ cm C $30\pi$ cm D $19\pi$ cm
4

In the same circle, selected arcs $A$ and $B$ have central turns $\pi/5$ and $2\pi/3$ radians respectively. What is the ratio of length $A$ to length $B$ ?

Answer choices for question 4 A $2:15$ B $3:10$ C $10:3$ D $5:3$
5

One selected arc has radius $11$ cm and central turn $4/7$ radian. Another has radius $22$ cm and central turn $2/7$ radian. How do their lengths compare?

Answer choices for question 5 A The second is twice the first. B The second is half the first. C The lengths are equal. D The second is four times the first.
6

Convert $294^\circ$ to radians exactly.

Answer choices for question 6 A $\tfrac{30\pi}{49}$ B $\tfrac{49\pi}{60}$ C $\tfrac{49}{30}$ D $\tfrac{49\pi}{30}$
7

Convert $\tfrac{13\pi}{15}$ radians to degrees.

Answer choices for question 7 A $78^\circ$ B $156^\circ$ C $195^\circ$ D $13^\circ$
8

A circle has circumference $30\pi$ cm. Find the length of a selected arc with central turn $11\pi/6$ radians.

Answer choices for question 8 A $\tfrac{55\pi}{2}$ cm B $55\pi$ cm C $\tfrac{5\pi}{2}$ cm D $\tfrac{11\pi}{6}$ cm
9

A circle has radius $7.5$ cm. Find the length of a selected arc with central turn $2.2$ radians.

Answer choices for question 9 A $\tfrac{22}{75}$ cm B $33$ cm C $\tfrac{75}{22}$ cm D $16.5$ cm
10

A circle has radius $13$ cm. What is the length along its selected minor arc of central turn $\pi/3$ radians?

Answer choices for question 10 A $13$ cm B $\tfrac{26\pi}{3}$ cm C $\tfrac{13\pi}{3}$ cm D $\tfrac{13\pi}{6}$ cm
11

In a circle of radius $8$ cm, the minor arc from $A$ to $B$ is $10\pi/3$ cm long. Find the length of the major arc with the same endpoints.

Answer choices for question 11 A $\tfrac{38\pi}{3}$ cm B $\tfrac{14\pi}{3}$ cm C $\tfrac{10\pi}{3}$ cm D $\tfrac{48\pi}{3}$ cm
12

A selected arc in a circle of radius $22$ cm occupies $3/8$ of a full turn. Which pair gives its radian measure and arc length?

Answer choices for question 12 A $\tfrac{3\pi}{4}$ radians; $33\pi$ cm B $\tfrac{3\pi}{4}$ radians; $\tfrac{33\pi}{2}$ cm C $\tfrac{3\pi}{8}$ radians; $\tfrac{33\pi}{2}$ cm D $\tfrac{3\pi}{8}$ radians; $33\pi$ cm