Worksheet: Perimeter of a Sector

In this worksheet, we will practice finding the perimeter of a sector given the radius, the diameter, the central angle, and/or the arc length or vice versa.

Q1:

𝑀 𝐴 𝐵 is a right-angled triangle at 𝑀 with an area of 58 cm2. Find the perimeter of the coloured part of the figure giving the answer to two decimal places.

Q2:

Work out the perimeter of the given shape, giving your answer accurate to two decimal places.

Q3:

A circle has a diameter of 32 cm and the central angle of a circular sector is 1 5 4 . Find the perimeter of the sector, giving the answer to the nearest centimetre.

Q4:

The arc length of a sector is 49 cm where the central angle is 1 8 0 . Find the perimeter of the circle giving the answer to the nearest centimetre.

Q5:

What is the formula for the perimeter of a sector with radius 𝑟 and arc length 𝑙 ?

  • A 2 𝑙 + 𝑟
  • B 1 2 𝑟 𝜃 rad
  • C 1 2 𝑟 𝜃 rad
  • D 2 𝑟 + 𝑙
  • E 2 𝜋 𝑟 𝑙

Q6:

The radius of a circle is 40 cm and the perimeter of a sector is 106 cm. Find the central angle in degrees giving the answer to the nearest second and in radians giving the answer to one decimal place.

  • A 3 7 1 4 3 2 , 0 . 3 r a d
  • B 1 8 3 7 1 6 , 0 . 7 r a d
  • C 1 8 3 7 1 6 , 0 . 3 r a d
  • D 3 7 1 4 3 2 , 0 . 7 r a d

Q7:

The radius of a circle is 3 0 𝑟 and the arc length of a sector is 4 4 𝑙 . Find the perimeter of the sector in terms of 𝑟 and 𝑙 .

  • A 4 ( 1 5 𝑙 + 1 1 𝑟 )
  • B 1 5 𝑟 + 1 1 𝑙
  • C 1 5 𝑙 + 1 1 𝑟
  • D 4 ( 1 5 𝑟 + 1 1 𝑙 )

Q8:

The perimeter of a circular sector is 47 cm and the arc length is 25 cm. Find the radius of the circle giving the answer to the nearest centimetre.

Q9:

The arc length of a sector is 33 cm, and the perimeter is 67 cm. Find the central angle giving the answer to the nearest second.

  • A 2 4 8 4 6 4 4
  • B 2 9 3 0 5 8
  • C 3 3 0 2 9 2
  • D 1 1 1 1 3 1 6

Q10:

A semicircle has a radius of 9 inches.

Work out the length of the arc of the semicircle, giving your answer to two decimal places.

Work out the perimeter of the semicircle, giving your answer to two decimal places.

Q11:

In the given figure, 𝑚 𝐵 𝐴 𝐶 = 3 0 , 𝐴 𝐵 = 7 , and 𝐴 𝐷 = 4 .

Work out the perimeter of 𝐵 𝐷 𝐸 𝐶 . Give your answer to 2 decimal places.

Work out the area of 𝐵 𝐷 𝐸 𝐶 . Give your answer to 2 decimal places.

Q12:

Find the circumference of the circular sector whose arc length is 12 cm and angle is 6 0 .

  • A 18 cm
  • B 72 cm
  • C 9 cm
  • D 36 cm

Q13:

What is the definition of a circular sector?

  • Athe region of a circle bounded by two radii and a chord
  • Bthe region of a circle bounded by an arc and a chord passing by the ends of this arc
  • Can arc which is half of the circumference
  • Dthe region of a circle bounded by two radii and an arc
  • Ea part of the circumference between two points or a continuous piece of a circle

Q14:

𝑀 𝐴 𝐵 is a right-angled triangle at 𝑀 with an area of 46 cm2. Find the perimeter of the coloured part of the figure giving the answer to two decimal places.

Q15:

The radius of a circle is 46 cm and the perimeter of a sector is 130 cm. Find the central angle in degrees giving the answer to the nearest second and in radians giving the answer to one decimal place.

  • A 4 7 1 9 5 3 , 0 . 4 r a d
  • B 2 3 3 9 5 6 , 0 . 8 r a d
  • C 2 3 3 9 5 6 , 0 . 4 r a d
  • D 4 7 1 9 5 3 , 0 . 8 r a d

Q16:

The arc length of a sector is 4 cm where the central angle is 1 8 0 . Find the perimeter of the circle giving the answer to the nearest centimetre.

Q17:

The arc length of a sector is 34 cm, and the perimeter is 88 cm. Find the central angle giving the answer to the nearest second.

  • A 2 8 7 5 0 5 9
  • B 4 5 2 9 5 9
  • C 3 1 4 3 0 1
  • D 7 2 9 1

Q18:

The perimeter of a circular sector is 96 cm and the arc length is 20 cm. Find the radius of the circle giving the answer to the nearest centimetre.

Q19:

A circle has a diameter of 24 cm and the central angle of a circular sector is 3 7 . Find the perimeter of the sector, giving the answer to the nearest centimetre.

Q20:

A circle has a diameter of 48 cm and the central angle of a circular sector is 6 2 . Find the perimeter of the sector, giving the answer to the nearest centimetre.

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