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In the figure (ii) given below, the inside perimeter of a practice running track with semi-circular ends and straight parallel sides is 312 m. The length of thestraight portion of the track is 90 m. If the track has a uniform width of 2 mthroughout, find its area. |
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Answer» hope this will HELP you PLEASE mark me brainlist and follow me Step-by-step explanation: The length of the STRAIGHT portion of the track is 90 m.and The inside perimeter 312m ∴πr+length+πr+length=312 ⇒πr+90+πr+90=312 ⇒2πr=312−180 ⇒2πr=132 ⇒r= 2π 132
⇒r= 2×22 132×7
⇒r= 44 924
⇒r=21 Width of the RUNNING track =2m ∴ Radius of outer perimeter=21+2=23 ∴ Area of outer perimeter = 2 π(23) 2
+(90×23×2)+ 2 π(23) 2
= 7×2 22(23) 2
+(90×23×2)+ 7×2 22(23) 2
=831.285+4140+831.285=5802.57 ∴ Area of inner perimeter = 2 π(21) 2
+(90×21×2)+ 2 π(21) 2
= 7×2 22(21) 2
+(90×21×2)+ 7×2 22(21) 2
=693+3780+693=5166 Area of the track= Area of outer perimeter − Area of inner perimeter =5802.57−5166 =636.57m 2
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