# AB is the chord of a circle of centre O and radius 4 cm. AB is of length 4 cm. Find the area of the sector of the circle formed by chord AB.

Last updated date: 25th Mar 2023

•

Total views: 306.3k

•

Views today: 7.84k

Answer

Verified

306.3k+ views

Hint: Use the information, area of the sector $ = \dfrac{\theta }{{{{360}^ \circ }}} \times \pi {r^2}$ and area of the circle with radius r is $\pi {r^2}$.

Complete step-by-step answer:

Given the radius of the circle $r = 4cm$ and length of chord $ = 4cm$ $\therefore $ the triangle formed is an equilateral triangle. $\therefore \theta = {60^ \circ }$ because every angle of the equilateral triangle is ${60^ \circ }$. Now, we know that the area of the sector $ = \dfrac{\theta }{{{{360}^ \circ }}} \times \pi {r^2}$. Where, $\theta $ is angle subtended at a centre and $\pi {r^2}$ is the area of the circle. On putting the values,

$\dfrac{\theta }{{{{360}^ \circ }}} \times \pi {r^2} \Rightarrow \dfrac{{{{60}^ \circ }}}{{{{360}^ \circ }}} \times \dfrac{{22}}{7} \times {4^2} = 8.38c{m^2}$

Note: There are lots of variations of this question but the core concept is the same. We’ll be having some values, then we need to use the correct formula to get the value of known.

Complete step-by-step answer:

Given the radius of the circle $r = 4cm$ and length of chord $ = 4cm$ $\therefore $ the triangle formed is an equilateral triangle. $\therefore \theta = {60^ \circ }$ because every angle of the equilateral triangle is ${60^ \circ }$. Now, we know that the area of the sector $ = \dfrac{\theta }{{{{360}^ \circ }}} \times \pi {r^2}$. Where, $\theta $ is angle subtended at a centre and $\pi {r^2}$ is the area of the circle. On putting the values,

$\dfrac{\theta }{{{{360}^ \circ }}} \times \pi {r^2} \Rightarrow \dfrac{{{{60}^ \circ }}}{{{{360}^ \circ }}} \times \dfrac{{22}}{7} \times {4^2} = 8.38c{m^2}$

Note: There are lots of variations of this question but the core concept is the same. We’ll be having some values, then we need to use the correct formula to get the value of known.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

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

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE