SOLUTION: A running track 5 m wide goes around a soccer field that is twice as long as it is wide. At each end of the soccer field the track is a semi-circle with inner radius r. Find a form

Question 699473: A running track 5 m wide goes around a soccer field that is twice as long as it is wide. At each end of the soccer field the track is a semi-circle with inner radius r. Find a formula for the area of the tracks in terms pi and r
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
The width of the track is 2*r, so the lenght is 4*r. The area of the two straight sections of the track, alomg the lenght is
(1) Asides = 2*5*4*r or 40r
The ends butted together form a "donut" with inner circle of radius r and an outer circle of (r+5), giving the area of the ends as
(2) Aends = pi*((5+r)^2) - pi*(r^2) or
(3) Aends = pi*(25 + 10*r)
The total area of the track is (1) plus (3) or
(4) Atotal = 40*r + pi*(25 + 10*r)
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