The Area of a Sector of a Circle of 6 Cm Radius is 15 π Sq.Cm. Find the Measure of the Arc and Length of the Arc Corresponding to the Sector. - Geometry

Question

The area of a sector of a circle of 6 cm radius is 15 $\pi$ sq.cm. Find the measure of the arc and length of the arc corresponding to the sector.

Solution

The radius of the sector, r = 6 cm
Let the measure of the arc be θ and the length of the arc corresponding to the sector be l cm.
Area of the sector = 15 $\pi$ cm2         (Given)

$\therefore \frac{1}{2}lr = 15\pi$
$\Rightarrow \frac{1}{2} \times l \times 6 = 15\pi$
$\Rightarrow l = \frac{15\pi}{3} = 5\pi \text{ cm}$

Length of the arc = $5\pi \text{ cm}$

$\therefore \frac{\theta}{360°} \times 2\pi r = 5\pi$
$\Rightarrow \theta = \frac{5 \times 360°}{2r}$
$\Rightarrow \theta = \frac{5 \times 360° }{2 \times 6}$
$\Rightarrow \theta = 150°$

Thus, the measure of the arc and length of the arc corresponding to the sector are 150º and 5 $\pi$ cm, respectively.

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The Area of a Sector of a Circle of 6 Cm Radius is 15 π Sq.Cm. Find the Measure of the Arc and Length of the Arc Corresponding to the Sector. Concept: Surface Area of a Combination of Solids.