(24 = 3) + 3 + 33 Your answer
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Answer:
Circumference(C) of the circle is given by:
where, r is the radius of the circle.
As per the statement:
A circular swimming pool has a radius of 15 ft.
⇒radius of the pool(r) = 15 ft
There is a path all around that pool that is three feet wide.
⇒radius of the outer edge of the path around the pool(r') = 15 +3 = 18 ft
Substitute these in the formula we have;
⇒
Therefore, the circumference of the outer edge of the path around the pool is, 113.04 ft
The area of the surface is given exactly by the integral,
We have
so the area is
We split up the domain of integration into 10 subintervals,
[0, 1/2], [1/2, 1], [1, 3/2], ..., [4, 9/2], [9/2, 5]
where the left and right endpoints for the -th subinterval are, respectively,
with midpoint
with .
Over each subinterval, we interpolate with the quadratic polynomial,
Then
It turns out that the latter integral reduces significantly to
which is about 651.918, so that the area is approximately .
Compare this to actual value of the integral, which is closer to 1967.