Arc Length and Radians: Practice Level 3 | Geometry

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

A circle has radius $(2x+1)$ cm, where $x>-1/2$ . A selected arc has central turn $\pi/3$ radians and length $4\pi$ cm. Find $x$ .

Answer choices for question 1 A $12$ B $\tfrac{13}{2}$ C $11$ D $\tfrac{11}{2}$
2

Two selected arcs have equal length. Their positive radii are $(r+3)$ cm and $2r$ cm. Their central turns are $4\pi/9$ and $\pi/3$ radians respectively. Find $r$ .

Answer choices for question 2 A $3$ B $6$ C $9$ D $12$
3

A circle has radius $7$ cm. Can an arc of length $22\pi$ cm be traced along it once without repeating any part of the circle?

Answer choices for question 3 A Yes; it is a minor arc. B Yes; it is a semicircle. C No; the proposed length is greater than the circumference. D Yes; it is a major arc shorter than a full circle.
4

In a circle of radius $16$ cm, a minor central angle measures $5\pi/8$ radians. How much longer is the major arc between its endpoints than the minor arc?

Answer choices for question 4 A $12\pi$ cm B $10\pi$ cm C $22\pi$ cm D $32\pi$ cm
5

A circle has diameter $1.8$ m. Find the length of a selected $250^\circ$ arc, rounded to the nearest centimeter. Use a calculator value of $\pi$ .

Answer choices for question 5 A $196$ cm B $393$ cm C $785$ cm D $250$ cm
6

A circle has radius $18$ cm. The major arc between two endpoints is $12\pi$ cm longer than the minor arc. Find the minor arc's central turn in radians.

Answer choices for question 6 A $\tfrac{\pi}{3}$ B $\tfrac{4\pi}{3}$ C $\tfrac{5\pi}{3}$ D $\tfrac{2\pi}{3}$
7

A point travels one full lap of a circular track of radius $13$ m, then continues through another $120^\circ$ . Find the total distance traveled.

Answer choices for question 7 A $\tfrac{104\pi}{3}$ m B $\tfrac{26\pi}{3}$ m C $26\pi$ m D $\tfrac{52\pi}{3}$ m
8

Point $B$ lies on the selected minor arc from $A$ to $C$ . The arc from $A$ to $B$ is $7$ cm long and the arc from $B$ to $C$ is $9$ cm long. The whole selected arc has central turn $4/5$ radian. Find the radius.

Answer choices for question 8 A $16$ cm B $\tfrac{64}{5}$ cm C $20$ cm D $\tfrac52$ cm
9

The same central turn selects arcs in two circles. The larger radius is $7/3$ times the smaller radius. The larger arc is $24$ cm longer than the smaller arc. Find the smaller arc length.

Answer choices for question 9 A $18$ cm B $42$ cm C $32$ cm D $\tfrac{72}{7}$ cm
10

A circle has radius $45$ cm. Its selected minor arc is $36\pi$ cm long and its central angle is $(x+12)^\circ$ . Find $x$ .

Answer choices for question 10 A $144$ B $156$ C $132$ D $\tfrac45$
11

A circle has diameter $25$ cm. A selected major arc has central turn $3.8$ radians. Find the exact length of the minor arc with the same endpoints.

Answer choices for question 11 A $(25\pi-95)$ cm B $(25\pi-47.5)$ cm C $47.5$ cm D $(12.5\pi-47.5)$ cm
12

A circle has positive radius $(x+8)$ cm. A selected arc, traced once, has positive central turn $(x-3)$ radians and length $60$ cm. Find $x$ .

Answer choices for question 12 A $-12$ B $12$ C $-7$ D $7$