Question

28 multiple choice 2 points a cement walk 3 ft wide is placed around the outside of a circular pond with diameter 17 ft. what is the total cost of the walk if the cost per square foot is $1.81?

Explanation:

Step1: Find the radius of the pond

The diameter of the pond \(d = 17\) ft, so the radius of the pond \(r=\frac{d}{2}=\frac{17}{2}=8.5\) ft.

Step2: Find the radius of the outer - circle (pond + walk)

The width of the walk is \(3\) ft. So the radius of the outer - circle \(R=r + 3=8.5+3 = 11.5\) ft.

Step3: Calculate the area of the walk

The area of a circle is \(A=\pi r^{2}\). The area of the walk \(A=\pi R^{2}-\pi r^{2}=\pi(R^{2}-r^{2})\).
Using the difference of squares formula \(a^{2}-b^{2}=(a + b)(a - b)\), where \(a = R\) and \(b = r\). So \(A=\pi(R + r)(R - r)\).
Substitute \(R = 11.5\) ft and \(r = 8.5\) ft. Then \(A=\pi(11.5 + 8.5)(11.5-8.5)=\pi\times20\times3=60\pi\) square feet.
Take \(\pi\approx3.14\), so \(A\approx60\times3.14 = 188.4\) square feet.

Step4: Calculate the total cost

The cost per square foot is \(C=\$1.81\). The total cost \(T=A\times C\).
Substitute \(A = 188.4\) and \(C = 1.81\). Then \(T=188.4\times1.81=(190 - 1.6)\times1.81=190\times1.81-1.6\times1.81\).
\(190\times1.81=(200 - 10)\times1.81=200\times1.81-10\times1.81=362-18.1 = 343.9\), \(1.6\times1.81=(1 + 0.6)\times1.81=1.81+1.086 = 2.896\).
\(T=343.9-2.896=341.004\approx341\)

Answer:

\(\$341\)