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Lesson Worksheet: Areas of Circular Sectors Mathematics

In this worksheet, we will practice finding the area of a circular sector and solving problems that relate this area to the arc length and perimeter of the sector.

Q1:

Write an expression for the area of a sector whose arc’s measure is πœƒ radians, knowing that the expression for the area of a sector measuring πœƒ degrees is πœ‹π‘Ÿπœƒ360.

  • A12π‘ŸπœƒοŠ¨
  • B12π‘Ÿπœƒ
  • C2π‘Ÿπœƒ
  • D2π‘ŸπœƒοŠ¨
  • E14π‘ŸπœƒοŠ¨

Q2:

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

Q3:

The radius of a circle is 21 cm and the angle of a sector is 123∘. Find the area of the sector giving the answer to the nearest square centimeter.

Q4:

An arc has a measure of πœ‹3 radians and a radius of 5. Give the area of the sector, in terms of πœ‹, in its simplest form.

  • A25πœ‹3
  • B50πœ‹3
  • C25πœ‹6
  • D50πœ‹6
  • E5πœ‹2

Q5:

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

Q6:

The area of a circular sector is 14 of the area of a circle, find, in radians, the central angle, correct to one decimal place.

Q7:

Given that the area of the colored part in the figure is 155 cm2, find the value of π‘₯ to the nearest tenth.

Q8:

A landscape gardener decides that he wants to design a lawn split into a series of sectors with circular patios laid into the grass, as shown in the given figure. The circular lawn will be split into six equal sectors, each with a radius of eight meters. The lines 𝑂𝐴 and 𝑂𝐡 are both tangents to the circle, and the arc 𝐴𝐡 touches the circle at a single point.

Work out the area of sector 𝑂𝐴𝐡. Give your answer in terms of πœ‹.

  • A64πœ‹3 square meters
  • B8πœ‹3 square meters
  • C32πœ‹7 square meters
  • D32πœ‹3 square meters
  • E4πœ‹3 square meters

The gardener needs to calculate the radius of the circular patio. Using trigonometric ratios, calculate the radius of the patio. Give your answer as a fraction.

  • A83 meters
  • B38 meters
  • C163 meters
  • D43 meters
  • E34 meters

Calculate the total area of grass in one sector. Give your answer, in terms of πœ‹, in its simplest form.

  • A64πœ‹9 square meters
  • B32πœ‹9 square meters
  • C329 square meters
  • D32πœ‹3 square meters
  • E9πœ‹32 square meters

Q9:

Three congruent circles with a radius of 43 cm are placed touching each other. Find the area of the part between the circles giving the answer to the nearest square centimeter.

Q10:

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

This lesson includes 55 additional questions and 461 additional question variations for subscribers.

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