SOLUTION: If Mario plans to develop a circular race track 0.75mi in circumference on a square plot of land, then what is the minimum number of acres that he needs? (One acre is equal to 43,5
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Question 1144568: If Mario plans to develop a circular race track 0.75mi in circumference on a square plot of land, then what is the minimum number of acres that he needs? (One acre is equal to 43,560ft^2). Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
(1) Convert the circumference of 0.75 miles to feet (1 mile = 5280 feet).
(2) Divide by 2pi to find the radius.
(3) The area is pi times the radius squared.
(4) Convert that area in square feet to acres by dividing by 43560.
You can do those calculations as easily as we can....
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Tutor @ikleyn is right.... I have a bad habit of not reading the whole problem -- I didn't see that the problem was asking for the area of a square plot of land on which the race track could be built.
So, as she says, divide the circumference by pi to get the diameter, which will be the length of a side of the square; then square that to get the area in square feet, and finally convert to acres by dividing by 43560.
My understanding is that in the problem, the circle is INSCRIBED into the square.
Then the calculations are as follows :
(1) The diameter of the circle d = = = 0.238854 miles = 0.238854*5280 feet = 1261.15 feet.
(2) Hence, the side of the square plot of land is
a = d = 1261.15 feet.
(3) Then the area of the square plot of land is
area = = = 1590497 square feet = acres = 36.513 acres. ANSWER
