(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

The diagram below is formed by three semicircles. If $OA = OB = 70\, cm,$ find the area of the figure formed (in $cm^2$).

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In the adjoining figure,$PS$ is the diameter of a circle and $PS = 12$. $PQ = QR = RS$. Semicircles are drawn with diameters $\overline{PQ}$ and $\overline{QS}$. Find the perimeter and the area of the shaded region. $(\pi = 3.14)$

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$A$ calf is tied with a rope of length $6 \,m$ at the corner of a square grassy lawn of side $20 \,m$. If the length of the rope is increased by $5.5 \,m$,find the increase in area of the grassy lawn in which the calf can graze. (in $m^2$)

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Points $A$ and $B$ are distinct points on $\odot(O, r)$ and point $C$ on the circle lies in the interior of $\angle AOB$. Then,$\overline{AB} \cup \widehat{ACB}$ is ........

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The diameter of a circle with area $38.5 \, m^2$ is $\ldots \ldots \ldots \ldots m$.

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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

The diagram below is formed by three semicircles. If $OA = OB = 70\, cm,$ find the area of the figure formed (in $cm^2$).

In the adjoining figure,$PS$ is the diameter of a circle and $PS = 12$. $PQ = QR = RS$. Semicircles are drawn with diameters $\overline{PQ}$ and $\overline{QS}$. Find the perimeter and the area of the shaded region. $(\pi = 3.14)$

$A$ calf is tied with a rope of length $6 \,m$ at the corner of a square grassy lawn of side $20 \,m$. If the length of the rope is increased by $5.5 \,m$,find the increase in area of the grassy lawn in which the calf can graze. (in $m^2$)

Points $A$ and $B$ are distinct points on $\odot(O, r)$ and point $C$ on the circle lies in the interior of $\angle AOB$. Then,$\overline{AB} \cup \widehat{ACB}$ is ........

The diameter of a circle with area $38.5 \, m^2$ is $\ldots \ldots \ldots \ldots m$.

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