Question

The area of a circle is 81 pi sq. Cms. Find the length of the arc subtending an angle of 300 degree at the centre and the area of corresponding sector .

Answer 1

πr^2 = 81π then r = 9 cm
then circumference of 300° degree subtending arc = 2π/(5π/3) *π*r = 6/5*π*r =
10.8π cm
and corresponding area = (π-π/6) *r^2 =
5π/6 *r^2 = 5π/6 *81 = 67.5π cm^2.

Answer 2

Answer:

The arc length is 1522.8 cm and Area of sector is $67.4817 cm^2$

Step-by-step explanation:

The area of a circle is 81 pi sq. cm.

Area of circle = $\pi r^2$

So, $81=\pi r^2$

$81=\frac{22}{7}r^2$

$81\times \frac{7}{22}=r^2$

$25.7727=r^2$

$\sqrt{25.7727}=r$

$5.076 =r$

Formula of arc length = $s= r \theta$

So, Arc length = $5.076 \times 300=1522.8$

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

                       = $\frac{300 }{360} \times \frac{22}{7} \times (5.076 )^2$

                       = $67.4817 cm^2$

Hence The arc length is 1522.8 cm and Area of sector is $67.4817 cm^2$