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The perimeter of a sector of a circle of radius 14cm is 68cm. Find the area of the sector. |
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Answer» Given : The perimeter of a sector of a circle of radius 14 CM is 68 cm.To Find : The area of the sector ?Solution :Perimeter of a sector = Twice of radius + LENGTH of arci.e. P=2r+lP=2r+l68=2(14)+l68=2(14)+ll=68-28l=68−28l=40l=40The length of arc is 40 cm.The formula of length of arc is l=\frac{\theta}{360}\times 2\pi rl= 360θ ×2πr40=\frac{\theta}{360}\times 2\times\frac{22}{7}\times 1440= 360θ ×2× 722 ×1440=\frac{\theta}{360}\times 8840= 360θ ×88\theta=\frac{40\times 360}{88}θ= 8840×360 \theta=\frac{3600}{22}θ= 223600 The area of the sector is A=\frac{\theta}{360}\times \pi r^2A= 360θ ×πr 2 A=\frac{\frac{3600}{22}}{360}\times\frac{22}{7}\times 14\times 14A= 360223600 × 722 ×14×14A=280\ cm^2A=280 cm 2 THEREFORE, the area of the sector is 280 cm². |
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