Perimeter for a Sector and a Segment

Q. Given that a pizza has a radius of 6 inches and has 6 slices, what is the perimeter of one of the slices of pizza?

1. $(\pi +6)\mathrm{inches}$
2. $2(\pi +6)\mathrm{inches}$
3. $2(\pi +8)\mathrm{inches}$
4. $(\pi +8)\mathrm{inches}$

Q.

Find the perimeter of the minor sector $OAB$ shown below.

cm

Q. The perimeter of a circle of diameter $d$ and radius $r$ can be written as

1. $\pi r$
2. $2\pi d$
3. $\frac{\pi d}{2}$
4. $\pi d$

Q. An minor arc subtends an angle of ${60}^{\circ }$ at the centre of the circle with radius $3$ units. What is the arc length of the major sector?

1. $4\pi \mathrm{units}$
2. $5\pi \mathrm{units}$
3. $6\pi \mathrm{units}$
4. $7\pi \mathrm{units}$

Q. What is the perimeter of a segment whose end points subtend a ${60}^{\circ }$ angle at the center of a circle of diameter $3$ inches?

1. $\frac{\pi }{2}+6$ inches
2. $\frac{\pi }{2}+\frac{3}{2}$ inches
3. $\frac{\pi }{2}+3$ inches

Q. What is the perimeter of a sector whose end points subtend a ${45}^{\circ }$ angle at the center of a circle of radius $8$ inches?

1. $14+2\pi$ inches
2. $14+4\pi$ inches
3. $16+2\pi$ inches
4. $16+4\pi$ inches

Q. Given that a circle has a radius $r$ and a sector that subtends an acute angle $\theta$ at the centre of the circle, then the perimeter of the sector is given by which of the following?

1. $d(1+\frac{\theta \pi }{{180}^{\circ }})$
2. $d(1+\frac{\theta \pi }{{360}^{\circ }})$
3. $r(1+\frac{\theta \pi }{{360}^{\circ }})$
4. $r(1+\frac{\theta \pi }{{180}^{\circ }})$

Q. Given that a chord with length $l$ subtends an angle $\theta$ at the centre of the circle with diameter $d$ and radius $r$, find the perimeter of the segment.

1. $\frac{\theta }{{360}^{\circ }}\times \pi r+l$
2. $\frac{\theta }{{360}^{\circ }}\times \pi d+l$
3. $\frac{\theta }{{180}^{\circ }}\times \pi r+l$

Q. A chord of length $14$ units subtends a $\angle {120}^{\circ }$ in a circle with radius $r=9$ units. What is the perimeter of the segment?

1. $6\pi +12\mathrm{units}$
2. $6\pi +14\mathrm{units}$
3. $8\pi +12\mathrm{units}$
4. $8\pi +14\mathrm{units}$

Q. Find the perimeter of the minor segment $ACB$ shown below.

1. $2\pi +3\text{cm}$
2. $2\pi +6\text{cm}$
3. $\pi +12\text{cm}$
4. $\pi -6\text{cm}$

Q. Perimeter of a segment is $5(\pi +2)\text{m}.$ If the angle subtended by a segment at the centre of the circle is ${180}^{\circ },$ the the radius of the circle is m.

Q. If the radius of a circle is $r,$ then:

1. the value of the perimeter of a sector is always greater than $2r$
2. the value of the perimeter of a sector is always greater than $2\pi r$
3. the value of the perimeter of a sector is always less than $2\pi r$
4. the value of the perimeter of a sector is always less than $2r+2\pi r$