(A) Given: Radius $r = 6.3 \ cm$,Central angle $\theta = 150^{\circ}$.Length of the arc $l = \frac{\theta}{360^{\circ}} \times 2\pi r = \frac{150}{360

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(A) Given: Radius $r = 6.3 \ cm$,Central angle $\theta = 150^{\circ}$.Length of the arc $l = \frac{\theta}{360^{\circ}} \times 2\pi r = \frac{150}{360} \times 2 \times \frac{22}{7} \times 6.3 = \frac{5}{12} \times 2 \times 22 \times 0.9 = 16.5 \ cm$.Area of the sector $A = \frac{\theta}{360^{\circ}} \times \pi r^2 = \frac{150}{360} \times \frac{22}{7} \times 6.3 \times 6.3 = \frac{5}{12} \times 22 \times 0.9 \times 6.3 = 51.975 \ cm^2$.

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

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In a circle with radius $6.3 \ cm$,an arc subtends an angle of measure $150^{\circ}$ at the centre. Find the length of this arc and the area of the sector formed by this arc.

A
$16.5 \ cm, 51.975 \ cm^2$
B
$15.5 \ cm, 50.975 \ cm^2$
C
$17.5 \ cm, 52.975 \ cm^2$
D
$16.0 \ cm, 51.000 \ cm^2$

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Mix Examples - Areas Related to Circles

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In a circle with radius $6.3 \ cm$,an arc subtends an angle of measure $150^{\circ}$ at the centre. Find the length of this arc and the area of the sector formed by this arc.

Similar Questions

The length of the minute hand of a clock is $14\, cm$. The area of the region swept by it in $10$ minutes is $\ldots \ldots \ldots \, cm^2$.

$A$ running track is in the shape of a circular ring. The difference of its outer circumference and inner circumference is $44\,m$. Then,the width of the track is $\ldots \ldots \ldots \ldots\,m$.

As shown in the diagram,$\overline{ OA }$ and $\overline{ OB }$ are two radii of $\odot( O , 21 \text{ cm} )$ perpendicular to each other. If $OD = 10 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

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