Question

area of sector of a circle of radius 36cm is 54πcm².find the length of the corresponding arc of the sector.

Answer 1

Answer:

3π cm

Step-by-step explanation:

Find the area of the circle:

Area = πr²

Area = π(36)² = 1296π cm²

Find the fraction of the sector:

Sector = 54π/1296π  = 1/24

Find the length of the arc of the sector:

length of the arc = 1/24 x 2πr

length of the arc = 1/24 x 2π(36) = 3π cm

Answer: The length of the arc is 3π cm

Answer 2

Answer:

9.42 cm

Step-by-step explanation:

Hi,

Given Area of sector = r²∅/2 = 54π

Length of the arc of sector subtending an angle ∅ at its center is given by

l = r∅,

We know that Area of sector of a circle subtending an angle ∅ at its center

is given by

r²∅/2 = 54π

=> r∅ = 108π/r

Given radius of the circle, r = 36 cm

=> length of the arc of the sector , l is = 3π cm = 9.42 cm (approx).

Thus, the length of the corresponding arc of the sector is 9.42 cm.

Hope, it helped !