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Worksheet: Working with Radians

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 40 cm and the arc length of a sector is 12 cm. Find the area of the sector.

Q3:

A circle with radius 27 cm has a sector cut from it. The perimeter of the sector is 102 cm. What is the area of the sector?

Q4:

The area of a circular sector is 5 8 of the area of the circle. The radius is 27 cm. Find the central angle in radians giving the answer to two decimal places and the perimeter of the sector giving the answer to the nearest centimeter.

  • A πœƒ = 3 . 9 3 r a d r a d , perimeter = 1 3 3 c m
  • B πœƒ = 3 . 9 3 r a d r a d , perimeter = 2 3 9 c m
  • C πœƒ = 1 . 9 6 r a d r a d , perimeter = 1 0 7 c m
  • D πœƒ = 3 . 9 3 r a d r a d , perimeter = 1 6 0 c m
  • E πœƒ = 1 . 9 6 r a d r a d , perimeter = 1 3 3 c m

Q5:

The area of a circular sector is 1 8 of the area of the circle. The radius is 20 cm. Find the central angle in radians giving the answer to two decimal places and the perimeter of the sector giving the answer to the nearest centimeter.

  • A πœƒ = 0 . 7 9 r a d r a d , perimeter = 3 6 c m
  • B πœƒ = 0 . 7 9 r a d r a d , perimeter = 5 1 c m
  • C πœƒ = 0 . 3 9 r a d r a d , perimeter = 4 8 c m
  • D πœƒ = 0 . 7 9 r a d r a d , perimeter = 5 6 c m
  • E πœƒ = 0 . 3 9 r a d r a d , perimeter = 3 6 c m

Q6:

For a circle with radius π‘Ÿ , one radian is defined as the measure of an arc of length π‘Ÿ as shown in the given figure. Knowing that the circumference of a circle is 2 πœ‹ π‘Ÿ , what is the measure of a complete revolution of a circle in radians?

  • A πœ‹ 2
  • B πœ‹
  • C 2 πœ‹ π‘Ÿ
  • D 2 πœ‹
  • E πœ‹ π‘Ÿ

Q7:

A sector has an arc with a measure of 7 πœ‹ 8 radians and a radius of 7.

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

  • A 8 πœ‹
  • B πœ‹ 8
  • C 8 4 9 πœ‹
  • D 4 9 πœ‹ 8
  • E 3 4 3 πœ‹ 8

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

  • A 3 4 3 πœ‹ 1 6
  • B 3 4 3 1 6
  • C 3 4 3 πœ‹ 8
  • D 4 9 πœ‹ 8
  • E 1 6 πœ‹ 3 4 3

Q8:

The area of a circular sector is 1 888 cm2 and its central angle is 1.7 rad. Find the arc length of the sector giving the answer to the nearest centimeter.

  • A 20 cm
  • B 40 cm
  • C 160 cm
  • D 80 cm
  • E 227 cm

Q9:

The area of a circular sector is 142 cm2 and its central angle is 2.3 rad. Find the arc length of the sector giving the answer to the nearest centimeter.

  • A 6 cm
  • B 13 cm
  • C 51 cm
  • D 26 cm
  • E 72 cm

Q10:

The radius of a circle is 4 cm and the perimeter of a sector is 11 cm. Find the arc length of the sector giving the answer to the nearest centimetre.

Q11:

The radius of a circle is 42 cm and the perimeter of a sector is 122 cm. Find the arc length of the sector giving the answer to the nearest centimetre.

Q12:

is a circle with radius 35 cm and is an arc on with length 49 cm. Find the angle of the sector in radians giving the answer to one decimal place.

Q13:

The area of a circular sector is 16.5 cm2 and the area of the circle that contains the sector is 9 πœ‹ cm2. Find the perimeter of the circular sector.

Q14:

Determine the angle of the circular sector that represents 7 1 8 of the circle.

Q15:

The perimeter of a circular sector is 67 cm and the central angle is 0.31 rad. Find the radius of the sector giving the answer to the nearest centimeter.

  • A 58 cm
  • B 9 cm
  • C 16 cm
  • D 29 cm

Q16:

The perimeter of a circular sector is 44 cm and the central angle is 0.588 rad. Find the radius of the sector giving the answer to the nearest centimeter.

  • A 34 cm
  • B 10 cm
  • C 13 cm
  • D 17 cm

Q17:

The area of a circular sector is 252 cm2 and the radius is 42 cm. Find the perimeter of a sector giving the answer to the nearest centimeter.

  • A 30 cm
  • B 54 cm
  • C 143 cm
  • D 96 cm

Q18:

The arc length of a circular sector is 26 cm and the central angle is 2.36 rad. Find the area giving the answer to the nearest square centimeter and the perimeter of the sector giving the answer to the nearest centimeter.

  • A area = 1 4 3 c m 2 , perimeter = 3 7 c m
  • B area = 3 8 0 c m 2 , perimeter = 4 8 c m
  • C area = 7 6 0 c m 2 , perimeter = 7 0 c m
  • D area = 1 4 3 c m 2 , perimeter = 4 8 c m

Q19:

The arc length of a circular sector is 32 cm and the central angle is 4 rad. Find the area giving the answer to the nearest square centimeter and the perimeter of the sector giving the answer to the nearest centimeter.

  • A area = 1 2 8 c m 2 , perimeter = 4 0 c m
  • B area = 2 0 1 c m 2 , perimeter = 4 8 c m
  • C area = 4 0 2 c m 2 , perimeter = 6 4 c m
  • D area = 1 2 8 c m 2 , perimeter = 4 8 c m