Arc Length and Radians: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

Which condition defines a central angle of one radian?

Answer choices for question 1 A Its selected arc has the same length as the diameter. B Its selected arc has the same length as the radius. C Its chord has the same length as the radius. D Its selected arc is the whole circumference.
2

A selected arc is $14$ cm long in a circle of radius $7$ cm. What is its central angle in radians?

Answer choices for question 2 A $\tfrac12$ B $7$ C $98$ D $2$
3

Convert $60^\circ$ to radians.

Answer choices for question 3 A $\tfrac{\pi}{3}$ B $3\pi$ C $\tfrac{\pi}{6}$ D $60\pi$
4

Convert $\tfrac{5\pi}{4}$ radians to degrees.

Answer choices for question 4 A $125^\circ$ B $45^\circ$ C $225^\circ$ D $900^\circ$
5

Find the length of a $45^\circ$ arc in a circle of radius $12$ cm.

Answer choices for question 5 A $3\pi$ cm B $6\pi$ cm C $\tfrac32\pi$ cm D $24\pi$ cm
6

A selected central turn is $\tfrac35$ radian in a circle of radius $10$ m. Find the arc length.

Answer choices for question 6 A $\tfrac3{50}$ m B $6$ m C $\tfrac{50}{3}$ m D $12$ m
7

The same central angle cuts an arc of $5$ cm in a circle of radius $6$ cm. Find the matching arc length in a circle of radius $18$ cm.

Answer choices for question 7 A $17$ cm B $\tfrac53$ cm C $45$ cm D $15$ cm
8

A circle has positive radius. How far along it does a zero central turn travel?

Answer choices for question 8 A $r$ B $\pi r$ C $0$ D $2\pi r$
9

Which is the radian measure of one full turn?

Answer choices for question 9 A $2\pi$ cm B $2\pi$ radians C $360$ radians D $\pi$ radians
10

An arc length and radius are both measured in meters. What happens to the length units in the quotient used for radian measure?

Answer choices for question 10 A They cancel, while radians identify the angle measure. B The quotient has units of square meters. C The quotient keeps meters because the arc is curved. D The quotient has units of meters per radian.
11

A circle has diameter $20$ cm. Find the length of its selected $126^\circ$ arc.

Answer choices for question 11 A $14\pi$ cm B $\frac{7\pi}{2}$ cm C $7\pi$ cm D $20\pi$ cm
12

A selected arc has central turn $\tfrac{7\pi}{8}$ radians. What kind of arc is it?

Answer choices for question 12 A A semicircle B A major arc C A full circle D A minor arc