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Sectors, Segments, and Circular Regions: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

A proper sector has angle $5/4$ radians and complete perimeter $26$ cm. What is its area?

Answer choices for question 1 A $80\text{ cm}^2$ B $32\text{ cm}^2$ C $26\text{ cm}^2$ D $40\text{ cm}^2$
2

A sector has area $45\pi\text{ cm}^2$ and selected arc length $9\pi$ cm. What is its radius?

Answer choices for question 2 A $5\text{ cm}$ B $10\text{ cm}$ C $9\text{ cm}$ D $\sqrt{10}\text{ cm}$
3

A circle has radius $11$ cm and a chord of length $11$ cm. What is the area of the minor circular segment cut off by the chord?

Answer choices for question 3 A $(\frac{121\pi}{3}-\frac{121\sqrt3}{4})\text{ cm}^2$ B $(\frac{121\pi}{6}+\frac{121\sqrt3}{4})\text{ cm}^2$ C $(\frac{121\pi}{6}-\frac{121\sqrt3}{4})\text{ cm}^2$ D $(\frac{121\pi}{6}-\frac{121}{2})\text{ cm}^2$
4

A radius- $14$ cm circle has a chord of length $14\sqrt2$ cm. What is the complete perimeter of the minor circular segment?

Answer choices for question 4 A $(7\pi+14\sqrt2)\text{ cm}$ B $(14\pi+14\sqrt2)\text{ cm}$ C $(7\pi+28)\text{ cm}$ D $7\pi\text{ cm}$
5

An annulus has area $91\pi\text{ cm}^2$ and total boundary length $26\pi$ cm. What is its inner radius?

Answer choices for question 5 A $7\text{ cm}$ B $3\text{ cm}$ C $10\text{ cm}$ D $13\text{ cm}$
6

Two opposite minor segments are removed from a circle of radius $9$ cm. Each removed segment has a $90^\circ$ central angle. What is the area left between the two chords?

Answer choices for question 6 A $(\frac{81\pi}{2}-81)\text{ cm}^2$ B $(81\pi-162)\text{ cm}^2$ C $\frac{81\pi}{2}\text{ cm}^2$ D $(81+\frac{81\pi}{2})\text{ cm}^2$
7

A sector of angle $4$ radians is removed from a disk of radius $7$ cm. The rest is kept as one closed sector. Which pair gives the kept area and complete perimeter?

Answer choices for question 7 A
Area $49\pi-98\text{ cm}^2$ .

Perimeter $14\pi-14\text{ cm}$ .
B
Area $98\text{ cm}^2$ .

Perimeter $14\pi-14\text{ cm}$ .
C
Area $49\pi-98\text{ cm}^2$ .

Perimeter $14\pi-28\text{ cm}$ .
D
Area $98\text{ cm}^2$ .

Perimeter $14\pi-28\text{ cm}$ .
8

A $90^\circ$ sector of radius $a$ and a $40^\circ$ sector of radius $b$ have equal areas. Both radii are positive and use the same unit. What is the ratio $a:b$ ?

Answer choices for question 8 A $3:2$ B $4:9$ C $2:3$ D $9:4$
9

A quarter of an annulus has width $3$ cm and area $51\pi/4\text{ cm}^2$ . What is the outer radius?

Answer choices for question 9 A $7\text{ cm}$ B $17\text{ cm}$ C $10\text{ cm}$ D $6\text{ cm}$
10

One $90^\circ$ sector is removed from a disk. The kept $270^\circ$ sector has area $75\pi\text{ cm}^2$ . What is its complete perimeter?

Answer choices for question 10 A $(20+15\pi)\text{ cm}$ B $15\pi\text{ cm}$ C $(20+5\pi)\text{ cm}$ D $20\pi\text{ cm}$
11

A sector has radius $16$ cm and selected arc length $7\pi$ cm. What is its exact area?

Answer choices for question 11 A $112\pi\text{ cm}^2$ B $\frac{49\pi}{2}\text{ cm}^2$ C $\frac{7\pi}{2}\text{ cm}^2$ D $56\pi\text{ cm}^2$
12

A quarter of an annulus has inner radius $4$ cm and complete perimeter $(12+7\pi)$ cm. What is its exact area?

Answer choices for question 12 A $25\pi\text{ cm}^2$ B $21\pi\text{ cm}^2$ C $29\pi\text{ cm}^2$ D $84\pi\text{ cm}^2$

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