Question

The area of the circle is 81πsq. cm. Find the arc length of this circle thay subtends a central angle of theta = π/3

Answer 1

area of circle = 81 π cm²
⇒π r² = 81 π
⇒ r² = 81
⇒ r = 9 cm
now length of arc = (2π r)× (π/3)/(2 π)
                             =  π r/3
                             = π × 9 /3
                             = 3π 
∴ so length of arc subtending angle π/3 = 3π

Answer 2

Area = pi ( r )^2 = 81 ( pi ) => r = 9 cm

( arc length ) = ( angle subtnded ) * ( radius )

=> arc length = (pi / 3) * 9 = 3 ( pi ) = 3 * 3.1415 cm
= 9.4245 cm