(A) Given: Radius $r = 42 \, cm$ and central angle $\theta = 120^{\circ}$.Length of the arc $l = \frac{\theta}{360^{\circ}} \times 2\pi r = \frac{120^

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(A) Given: Radius $r = 42 \, cm$ and central angle $\theta = 120^{\circ}$.Length of the arc $l = \frac{\theta}{360^{\circ}} \times 2\pi r = \frac{120^{\circ}}{360^{\circ}} \times 2 \times \frac{22}{7} \times 42 = \frac{1}{3} \times 2 \times 22 \times 6 = 88 \, cm$.Area of the sector $A = \frac{\theta}{360^{\circ}} \times \pi r^2 = \frac{120^{\circ}}{360^{\circ}} \times \frac{22}{7} \times 42 \times 42 = \frac{1}{3} \times 22 \times 6 \times 42 = 22 \times 2 \times 42 = 1848 \, cm^2$.

Class 10 Mathematics Areas Related to Circles Mix Examples - Areas Related to Circles

Medium

In a circle with radius $42 \, cm$,an arc subtends an angle of $120^{\circ}$ at the centre. Find the length of this arc and the area of the sector formed by this arc.

A
$88 \, cm, 1848 \, cm^2$
B
$44 \, cm, 924 \, cm^2$
C
$176 \, cm, 3696 \, cm^2$
D
$88 \, cm, 924 \, cm^2$

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Areas Related to Circles

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Mix Examples - Areas Related to Circles

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In a circle with radius $42 \, cm$,an arc subtends an angle of $120^{\circ}$ at the centre. Find the length of this arc and the area of the sector formed by this arc.

Similar Questions

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16 \, m$ and $12 \, m$ in a locality. The radius of the new park would be (in $m$)

In $\odot(O, 4)$,$\widehat{ACB}$ is a minor arc and $m \angle AOB = 45^\circ$. Then,the length of minor $\widehat{ACB}$ is $\ldots \ldots \ldots \ldots$

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