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Question 458541: A grassy area is going to be planted inside the path of a racing track. The track is 10 feet wide. The maximum radii of the semicircle ends are both of length x, while the straight portions of the circuit are three times the length of the semicircle ends. Find the area of the section to be planted with grass as a function of the track's maximum radius, x.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A grassy area is going to be planted inside the path of a racing track. The track is 10 feet wide. The maximum radii of the semicircle ends are both of length x, while the straight portions of the circuit are three times the length of the semicircle ends. Find the area of the section to be planted with grass as a function of the track's maximum radius, x.
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x=radius
let L=length of area to be planted with grass
let W=width of area to be planted with grass
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length of semicircle ends=1/2(2πx)=πx=(1/2 of circumference)
L=3πx)
W=2x-20 (twice the radius-twice the width of the track)
Area=3πx(2x-20)=6πx^2-60πx=6πx(x-10)
ans:
Area to be planted with grass=6πx(x-10) ft^2
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