A train travels on a 30 mile long circular track that surrounds an entire city. What is the area of the city rounded to the nearest half mile?
C = pi * d
30 = 3.14d
9.55 = d
A = pi * r^2
A = 3.14 * 4.777^2
A = 3.14 ^ 22.82
A = ?
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To find the area of the city, you need to know the radius of the circular track that surrounds it. However, the information given in the question does not provide the radius directly. We need to use the fact that the track is 30 miles long to determine the radius.
The length of the circular track is equal to the circumference of a circle, which is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, C = 30 miles, so we have the equation 30 miles = 2πr.
To find the radius, we can rearrange the equation and solve for r. Divide both sides of the equation by 2π:
30 miles / (2π) = r
Now calculate the value:
r ≈ 4.77465 miles
Since we are rounding to the nearest half mile, we can round the radius to 4.5 miles.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the rounded radius, we have:
A ≈ 3.14 * (4.5 miles)^2
Calculating the value:
A ≈ 63.585 square miles
Rounding to the nearest half mile, the area of the city is approximately 64 square miles.