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Worksheet: Finding the Area of a Circular Sector

Q1:

What is the area of a circular sector with a radius of length and a central angle of size ?

  • A
  • B
  • C
  • D

Q2:

Determine, to the nearest square yard, the area of the shaded sector of the shown circle.

Q3:

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

Q4:

Find the area of the shaded part of the diagram in terms of .

  • A cm2
  • B cm2
  • C cm2
  • D cm2

Q5:

Find the area of the shaded part of the diagram giving the answer to one decimal place.

Q6:

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

Q7:

An arc has a measure of radians and a radius of 5. Give the area of the sector, in terms of , in its simplest form.

  • A
  • B
  • C
  • D
  • E

Q8:

An arc has a measure of radians and a radius of 3. Work out the area of the sector, giving your answer in terms of and in its simplest form.

  • A
  • B
  • C
  • D
  • E

Q9:

The area of a circular sector is 1 790 cm2 and the central angle is 1.5 rad. Find the radius of the circle giving the answer to the nearest centimeter.

  • A 24 cm
  • B
    2 387
    cm
  • C 597 cm
  • D 49 cm

Q10:

The area of a circular sector is 1 943 cm2 and the central angle is 2.5 rad. Find the radius of the circle giving the answer to the nearest centimeter.

  • A 20 cm
  • B
    1 554
    cm
  • C 389 cm
  • D 39 cm

Q11:

The radius of a circle is 10 cm and the perimeter of a sector is 25 cm. Find the area of the sector.

Q12:

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

Q13:

The perimeter of a circular sector is 96 cm and the arc length is 36 cm. Find the area of the sector giving the answer to the nearest square centimeter.

  • A
  • B
  • C
  • D

Q14:

The radius of a circle is 12 cm and the angle of a sector is . Find the area of the sector giving the answer in terms of .

  • A cm2
  • B cm2
  • C cm2
  • D cm2

Q15:

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

Q16:

The radius of a circle is 5 cm and the area of a sector is 15 cm2. Find the central angle, in radians, rounded to one decimal place.

Q17:

The radius of a circle is 15 cm and the area of a sector is 630 cm2. Find the central angle, in radians, rounded to one decimal place.

Q18:

The area of a circular sector is 15 cm2 and the perimeter is 16 cm. Find all possible values for the central angle giving the answer to the nearest second.

  • A or
  • B or
  • C or
  • D or

Q19:

The area of a circular sector is 10 cm2 and the perimeter is 13 cm. Find all possible values for the central angle giving the answer to the nearest second.

  • A or
  • B or
  • C or
  • D or

Q20:

The area of a circular sector is of the circle it is in. Find the central angle giving the answer to the nearest second.

  • A
  • B
  • C
  • D

Q21:

The area of a circular sector is 612.5 cm2 and the area of the circle that contains the sector is cm2. Find the central angle giving the answer to the nearest degree.

Q22:

The area of a sector is cm2 where is the radius of the circle. Find the central angle giving the answer to the nearest degree.

  • A
  • B
  • C
  • D