(10) The perimeter of the sector of the circle
of area 640 sq.cm is 56 cm. Find the
area of the sector.
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Step-by-step explanation:
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^2Area of the circle=64πcm
2
\implies\:\pi\:r^2=64\pi⟹πr
2
=64π
\implies\:r=8\: cm⟹r=8cm
Also, Perimter of the sector = 56 cm
\implies\:2r+l=56⟹2r+l=56
\implies\:2(8)+l=56⟹2(8)+l=56
\implies\:l=56-16⟹l=56−16
\implies\:l=40\:cm⟹l=40cm
\text{Area of the sector}=\frac{lr}{2}Area of the sector=
2
lr
\text{Area of the sector}=\frac{(40)(8)}{2}Area of the sector=
2
(40)(8)
\boxed{\text{Area of the sector}=160\:cm^2}
Area of the sector=160cm
2
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