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Lesson: Applying the Arc Length Formula

Question Video: Finding the Length of the Arc given Its Central Angle’s Measure and Its Circle’s Radius

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Worksheet: Applying the Arc Length Formula • 17 Questions

Q1:

Write an expression for the length of an arc whose measure is radians, knowing that the expression for the length of an arc in degrees is .

  • A
  • B
  • C
  • D
  • E

Q2:

Find the length of the blue arc given the radius of the circle is 7 cm. Give the answer to one decimal place.

Q3:

Find the length of the blue arc given the radius of the circle is 5 cm. Give the answer to one decimal place.

Q4:

Find the length of the blue arc given the radius of the circle is 10 cm. Give the answer to one decimal place.

Q5:

In the given figure, the circumference is 15 and is . Find the length of .

  • A
  • B
  • C 5
  • D
  • E

Q6:

If and the radius of the circle equals 3 cm, find the length of the major arc .

Q7:

Given that , determine, to the nearest whole number, the length of arc and the area of the shaded region.

  • A 64 cm, 480 cm2
  • B 32 cm, 1 800 cm2
  • C 32 cm, 1 320 cm2
  • D 129 cm, 4 441 cm2

Q8:

What is the length of the arc of a circle of radius that is given by of the circumference?

  • A
  • B
  • C
  • D
  • E

Q9:

An arc has a measure of radians and a radius of 6. Work out the length of the arc, giving your answer in terms of , in its simplest form.

  • A
  • B
  • C
  • D
  • E

Q10:

An arc has a measure of radians and a radius of 9. Work out the length of the arc, giving your answer in terms of , in its simplest form.

  • A
  • B
  • C
  • D
  • E

Q11:

What is the length of the arc subtended by a central angle of on a circle of radius ?

  • A
  • B
  • C
  • D

Q12:

A circle has a central angle measuring which subtends an arc of length 21.18 cm. Find the radius of the circle giving the answer to the nearest centimeter.

  • A 17 cm
  • B 13 cm
  • C 34 cm
  • D 26 cm
  • E 9 cm

Q13:

A circle has a central angle measuring which subtends an arc of length 17.01 cm. Find the radius of the circle giving the answer to the nearest centimeter.

  • A 23 cm
  • B 6 cm
  • C 46 cm
  • D 13 cm
  • E 11 cm

Q14:

A circle has a radius of 14.49 cm. Find the central angle, in radians, that subtends an arc of length 8.23 cm, giving the answer to two decimal places.

Q15:

A circle has a radius of 8.8 cm. Find the central angle, in radians, that subtends an arc of length 6.36 cm, giving the answer to two decimal places.

Q16:

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

Q17:

The perimeter of a circular sector is 19 cm and the central angle is 0.375 rad. Find the arc length giving the answer to the nearest centimeter.

  • A 3 cm
  • B 8 cm
  • C 6 cm
  • D 16 cm
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