Question

Area of a sector of a circle of radius 36 cm is 54 pi cm2. Find the length of corresponding
arc of sector.

Answer 1

$area \: of \: sector = \frac{ \alpha }{360} \pi \: {r}^{2} \\ 54\pi = \frac{ \alpha }{360} \pi {36}^{2} \\ \alpha = \frac{54 \times 360}{36 \times 36} = \frac{90}{6} = 15 \\ length \: of \: arc = \frac{ \alpha }{360} \times 2\pi \: r \\ = \frac{15 \times 2 \times \pi \times 36}{360} \\ = 3\pi \: cm$

Answer 2

Answer:

$3\pi$

Step-by-step explanation:

Area of sector = $\frac{ \theta }{360} \pi {r}^{2}$

Area of a sector of a circle of radius 36 cm is 54 pi sq.cm.

$54 \pi=\frac{ \theta }{360} \pi {r}^{2}$

$54=\frac{ \theta }{360} {36}^{2}$

$\theta = 15$

Length of arc=$\frac{ \theta }{360}  \times 2\pi r$

Length of arc=$\frac{15}{360}  \times 2\pi (36)$

Length of arc=$3 \pi$

Hence the length of corresponding  arc of sector is $3\pi$