Question

The perimeter of the sector of the circle of area 64πsq.cm is 56 cm . find the area of the sector​

Answer 1

Answer:

$\text{Area of the sector}=160\:cm^2$

Step-by-step explanation:

The perimeter of the sector of the circle of area 64πsq.cm is 56 cm . find the area of the sector​

Let r be the radius of the given circle and l be the length of the arc of the sector

Given:

$\text{Area of the circle}=64\pi\:cm^2$

$\implies\:\pi\:r^2=64\pi$

$\implies\:r=8\: cm$

Also, Perimter of the sector = 56 cm

$\implies\:2r+l=56$

$\implies\:2(8)+l=56$

$\implies\:l=56-16$

$\implies\:l=40\:cm$

$\text{Area of the sector}=\frac{lr}{2}$

$\text{Area of the sector}=\frac{(40)(8)}{2}$

$\boxed{\text{Area of the sector}=160\:cm^2}$

Answer 2

Answer:

160 cm^2

Step-by-step explanation:

please see following attachment