Worksheet: Arc Lengths and Sectors: Degrees

In this worksheet, we will practice finding the arc length and the area of a sector given the angle measure in degrees.

Q1:

The radius of a circle is 28 cm and the arc length of a sector is 37 cm. Find the area of the sector.

Q2:

The radius of a circle is 12 cm and the angle of a sector is 115∘. Find the area of the sector giving the answer in terms of πœ‹.

  • A92πœ‹ cm2
  • B138πœ‹ cm2
  • C46πœ‹ cm2
  • D23πœ‹ cm2

Q3:

A circular birthday cake with a diameter of 22 cm is divided into eleven equal sectors. Using 3.14 as an approximation for πœ‹, find the area of one sector.

Q4:

The length of an arc in a circle is 120 of the circle’s circumference. Find the central angle subtending the arc giving the answer correct to the nearest degree.

Q5:

Shown is a sector of a circle. If its perimeter is 39 mm, what is its area?

Q6:

An arc has a measure of 286∘ and a radius of 4.5. Work out the area of the sector, in terms of πœ‹, in its simplest form.

  • A143πœ‹40
  • B143πœ‹20
  • C1,287πœ‹80
  • D1,287πœ‹40
  • E11,5834

Q7:

Circle 𝑀 has a diameter 𝐴𝐡 of length 36 cm where π‘šβˆ π΅π΄πΆ=46∘. Find the length of the minor arc 𝐴𝐢 in centimetres giving the answer to two decimal places.

Q8:

A squash player moves in an arc-shaped path in a circle of radius 1.6 meters with a rotation angle of 71∘. Find the length of the arc that the player makes giving the answer to one decimal place.

Q9:

𝐴𝐡𝐢 is a right-angled triangle at 𝐢 drawn inside a circle dividing the circle into three arcs where 𝐴𝐡=34cm and 𝐡𝐢=15cm. Find the lengths of the circle’s three minor arcs giving the answers to one decimal place.

  • Aarc 𝐡𝐢=7.8cm, arc 𝐴𝐢=37.9cm, arc 𝐴𝐡=26.7cm
  • Barc 𝐡𝐢=7.8cm, arc 𝐴𝐢=18.9cm, arc 𝐴𝐡=53.4cm
  • Carc 𝐡𝐢=15.5cm, arc 𝐴𝐢=37.9cm, arc 𝐴𝐡=53.4cm
  • Darc 𝐡𝐢=15.5cm, arc 𝐴𝐢=18.9cm, arc 𝐴𝐡=26.7cm

Q10:

An arc covers 29 of a circle’s circumference and the circle has a radius of 78 cm. Find the measure and the length of the arc using 227 as an approximation for πœ‹, rounding the length to the nearest hundredth..

  • A40∘, 54.45 cm
  • B80∘, 108.91 cm
  • C40∘, 108.91 cm
  • D80∘, 54.45 cm

Q11:

A circle has a radius of 5 cm and passes through the vertices of triangle 𝐴𝐡𝐢 where π‘šβˆ π΅π΄πΆ=34∘ and π‘šβˆ π΄π΅πΆ=52∘. Find the lengths of the circle’s three minor arcs giving the answers to one decimal place.

  • A𝐡𝐢=3.0cm, 𝐴𝐢=4.5cm, 𝐴𝐡=16.4cm
  • B𝐡𝐢=3.0cm, 𝐴𝐢=9.1cm, 𝐴𝐡=8.2cm
  • C𝐡𝐢=5.9cm, 𝐴𝐢=4.5cm, 𝐴𝐡=8.2cm
  • D𝐡𝐢=5.9cm, 𝐴𝐢=9.1cm, 𝐴𝐡=16.4cm

Q12:

𝐴𝐡 and 𝐴𝐢 are two tangents to the circle 𝑀 where 𝐴𝐡=14cm. Find the length of the major arc 𝐡𝐢 giving the answer to the nearest centimetre.

Q13:

𝑀𝐴𝐡 is a right triangle at 𝑀 with an area of 58 cm2. Find the perimeter of the colored part of the figure giving the answer to two decimal places.

Q14:

The arc length of a sector is 49 cm where the central angle is 180∘. Find the perimeter of the circle giving the answer to the nearest centimeter.

Q15:

The area of a circle is 160 cm2 and a central angle of a sector is 71∘. Find the area of the sector giving the answer to two decimal places.

Q16:

The radius of a circle is 16 cm and the angle of a sector is 45∘. Find the area of the sector giving the answer to the nearest square centimeter.

Q17:

Find the circumference of the circular sector whose arc length is 12 cm and angle is 60∘.

  • A9 cm
  • B72 cm
  • C18 cm
  • D36 cm

Q18:

An arc on a circle with a radius of 50 has a length of 115. Determine the arc’s measure to the nearest tenth of a degree.

Q19:

Determine, to the nearest tenth, the area of the shaded part in the given figure.

Q20:

An arc has a measure of 63∘ and a radius of 4.

Work out the length of the arc. Give your answer in terms of πœ‹ and in its simplest form.

  • A10πœ‹7
  • B7πœ‹5
  • C5πœ‹7
  • D7πœ‹10
  • E75

Work out the area of the sector. Give your answer in terms of πœ‹ and in its simplest form.

  • A14πœ‹5
  • B7πœ‹10
  • C7πœ‹5
  • D28πœ‹5
  • E288

Q21:

In this figure, the diameter of the larger circle is 41 cm and both circles have the same center. Determine, to the nearest tenth, the area of the shaded part.

Q22:

What is the formula for the perimeter of a sector with radius π‘Ÿ and arc length 𝑙?

  • A2𝑙+π‘Ÿ
  • B12π‘ŸπœƒοŠ¨ rad
  • C2π‘Ÿ+𝑙
  • D2πœ‹π‘Ÿπ‘™
  • E12π‘Ÿπœƒ rad

Q23:

An arc has a measure of 20∘ and a radius of 8. Calculate the length of the arc, in terms of πœ‹, in its simplest form.

  • A9πœ‹7
  • B9πœ‹8
  • C7πœ‹8
  • D8πœ‹9
  • E8πœ‹7

Q24:

Find the area of the shaded part in the figure. Round your answer to the nearest tenth.

Q25:

What is the definition of a circular sector?

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

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