Question

the area of the circle is 81 Pi square centimetre find the length of the arc substance and angle of the 300 degree at the centre of the also the area of the corresponding sector​

Answer 1

Answer:

length of arc = 47.1cm

area of sector = 212.14 sq cm

Step-by-step explanation:

area of circle = π × r^2 = 81π

r^2 = 81

r = √81

r = 9

length of arc = x/360 × 2 × π × r

$= \frac{300}{360} \times 2 \times \frac{22}{7} \times 9 \\ = \frac{5}{6} \times \frac{22}{7} \times 18 \\ = 5 \times \frac{22}{7} \times 3 \\ = 15 \times 3.14 \\ = 47.1cm$

area of the sector

$= \frac{x}{360} \times \pi \times {r}^{2} \\ = \frac{300}{360} \times \frac{22}{7} \times {9}^{2} \\ = \frac{5}{6} \times \frac{22}{7} \times 81 \\ = \frac{5}{2} \times \frac{22}{7} \times 27 \\ = 5 \times \frac{11}{7} \times 27 \\ = 212.14 \: {cm}^{2}$