Find the area of the minor segment of a circle of radius 14cm, when its central angle is ${60^0}$.Also find the area of the corresponding major segment. $\left[ {use{\text{ }}\pi {\text{ = }}\dfrac{{22}}{7}} \right]$
Answer
385.5k+ views
Hint-Simply use formulae of area of segment. This is the case of a circular segment which is cut off from the rest of the circle.
Now it has been given that the radius of the circle is 14cm and the central angle of the minor segment is ${60^0}$.
Now using the formulae that area of segment = $\pi {r^2}\left( {\dfrac{c}{{360}}} \right)$ where c is the central angle of segment
Area of minor segment = $\dfrac{{22}}{7} \times {(14)^2} \times \dfrac{{60}}{{360}}$
$ \Rightarrow \dfrac{{22 \times 2 \times 14}}{6} = 102.67c{m^2}$
Area of minor segment + area of major segment =Total area of the circle…………………….. (1)
Total area of circle $ = \pi {r^2}$
$ \Rightarrow \dfrac{{22}}{7} \times {\left( {14} \right)^2} = 22 \times 2 \times 14 = 616c{m^2}$
Using equation (1) area of major segment is
Total area of circle – area of minor segment
$ \Rightarrow 616 - 102.67 = 513.33c{m^2}$
Note – Whenever we face such problems the key concept is having the basic understanding of the formula for the area of segment when the central angle corresponding to a segment is given.

Now it has been given that the radius of the circle is 14cm and the central angle of the minor segment is ${60^0}$.
Now using the formulae that area of segment = $\pi {r^2}\left( {\dfrac{c}{{360}}} \right)$ where c is the central angle of segment
Area of minor segment = $\dfrac{{22}}{7} \times {(14)^2} \times \dfrac{{60}}{{360}}$
$ \Rightarrow \dfrac{{22 \times 2 \times 14}}{6} = 102.67c{m^2}$
Area of minor segment + area of major segment =Total area of the circle…………………….. (1)
Total area of circle $ = \pi {r^2}$
$ \Rightarrow \dfrac{{22}}{7} \times {\left( {14} \right)^2} = 22 \times 2 \times 14 = 616c{m^2}$
Using equation (1) area of major segment is
Total area of circle – area of minor segment
$ \Rightarrow 616 - 102.67 = 513.33c{m^2}$
Note – Whenever we face such problems the key concept is having the basic understanding of the formula for the area of segment when the central angle corresponding to a segment is given.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is pollution? How many types of pollution? Define it

Change the following sentences into negative and interrogative class 10 english CBSE

Why do noble gases have positive electron gain enthalpy class 11 chemistry CBSE

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE

Write an application to the principal requesting five class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers
