A rope of length 6 ft is arranged in the shape of a sector o

A rope of length 6 ft is arranged in the shape of a sector of a circle with the central angle 0 radians. Write the area of the sector A as a function of 0.

Solution

let \'r\' is the radius of a circle.

rope of length is given as 6ft.

the central angle may be (teeta) not 0 (zero)

if we proceed the central angle as radians,

it can be written as length of rope 6= r(2+)

that is r=6/2 =3

Arc length = 6/(+2)

A = Area = (1/2)*Arc*radius

A = (1/2)*6/(+2)*6/(+2)

A = 18/(+2)/(+2) = 18/(+2)^2

A(t) = 18/(+2)^2