(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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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 $5\, cm$. Find the area swept by the minute hand during the time period $6:05\, a.m.$ and $6:40\, a.m.$ (in $cm^2$).

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