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 arcβs measure is radians, knowing that the expression for the area of a sector measuring degrees is .
- A
- B
- C
- D
- E
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 . Find the area of the sector giving the answer to the nearest square centimeter.
Q4:
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
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 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 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 and are both tangents to the circle, and the arc touches the circle at a single point.
Work out the area of sector . Give your answer in terms of .
- A square meters
- B square meters
- C square meters
- D square meters
- E 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.
- A meters
- B meters
- C meters
- D meters
- E meters
Calculate the total area of grass in one sector. Give your answer, in terms of , in its simplest form.
- A square meters
- B square meters
- C square meters
- D square meters
- E 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.
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