Area and Perimeter of a Sector of a Circle

We will discuss the Area and perimeter of a sector of a circle

We know that

Area and Perimeter of a Sector of a Circle

Therefore,

Area of a sector of a circle = \(\frac{ \theta^{\circ}}{360^{\circ}}\) × Area of the circle = \(\frac{ θ}{360}\) ∙ πr2

where r is the radius of the circle and \(\theta^{\circ}\) is the sectorial angle.

Area and Perimeter of a Sector of a Circle

Also, we know that

Area of a Sector of a Circle

Therefore,

Arc MN = \(\frac{ \theta^{\circ}}{360^{\circ}}\) × Circumference of the circle = \(\frac{ θ}{360}\) ∙ 2πr = \(\frac{πθr}{180}\)

where r is the radius of the circle and \(\theta^{\circ}\) is the sectorial angle.

Thus,

perimeter of a sector of a circle = (\(\frac{πθ}{180}\) ∙ r + 2r) = (\(\frac{πθ}{180}\) + 2)r

where r is the radius of the circle and θ° is the sectorial angle.


Problems on Area and Perimeter of a Sector of a Circle:

1. A plot of land is in the shape of a sector of a circle of radius 28 m. If the sectorial angle (central angle) is 60°, find the area and the perimeter of the plot. (Use π = \(\frac{22}{7}\).)

Solution:

Area of the plot = \(\frac{60^{\circ}}{360^{\circ}}\) ×  πr2 [Since θ = 60]

                       = \(\frac{1}{6}\) ×  πr2

                       = \(\frac{1}{6}\) × \(\frac{22}{7}\) × 282 m2.

                       = \(\frac{1}{6}\) × \(\frac{22}{7}\) × 784 m2.

                       = \(\frac{17248}{42}\) m2.

                       = \(\frac{1232}{3}\) m2.

                       = 410\(\frac{2}{3}\) m2.

Perimeter of a Sector of a Circle


Perimeter of the plot = (\(\frac{πθ}{180}\) + 2)r

                              = (\(\frac{22}{7}\) ∙ \(\frac{60}{180}\) + 2) 28 m

                              = (\(\frac{22}{21}\) + 2) 28 m

                              = \(\frac{64}{21}\) ∙ 28 m

                              = \(\frac{1792}{21}\) m

                              = \(\frac{256}{3}\) m

                              = 85\(\frac{1}{3}\) m.






10th Grade Math

From Area and Perimeter of a Sector of a Circle to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Addition and Subtraction of Fractions | Solved Examples | Worksheet

    Jul 18, 24 03:08 PM

    Addition and subtraction of fractions are discussed here with examples. To add or subtract two or more fractions, proceed as under: (i) Convert the mixed fractions (if any.) or natural numbers

    Read More

  2. Worksheet on Simplification | Simplify Expressions | BODMAS Questions

    Jul 18, 24 01:19 AM

    In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet

    Read More

  3. Fractions in Descending Order |Arranging Fractions an Descending Order

    Jul 18, 24 01:15 AM

    We will discuss here how to arrange the fractions in descending order. Solved examples for arranging in descending order: 1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order. First…

    Read More

  4. Fractions in Ascending Order | Arranging Fractions | Worksheet |Answer

    Jul 18, 24 01:02 AM

    Comparison Fractions
    We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we fi…

    Read More

  5. Worksheet on Comparison of Like Fractions | Greater & Smaller Fraction

    Jul 18, 24 12:45 AM

    Worksheet on Comparison of Like Fractions
    In worksheet on comparison of like fractions, all grade students can practice the questions on comparison of like fractions. This exercise sheet on comparison of like fractions can be practiced

    Read More