Question

1 multiple choice 1 point
a cement walk 3 ft wide is placed around the outside of a circular pond with radius 17 ft. what is the total cost of the walk if the cost per square foot is $1.66?
$581.15
$582.73
$579.90
$583.38
$578.87
2 multiple choice 1 point
a golden rectangle is to be constructed such that the longest side is 11 inches long. how long is the other side? (round your answer to the nearest tenth of an inch)
6.0 inches
6.6 inches
6.4 inches
6.8 inches
6.2 inches

Explanation:

Step1: Find the radius of the outer - circle

The radius of the circular pond is $r = 17$ ft and the width of the walk is 3 ft. So the radius of the outer - circle $R=r + 3=17 + 3=20$ ft.

Step2: Calculate the area of the walk

The area of a circle is $A=\pi R^{2}-\pi r^{2}=\pi(R^{2}-r^{2})$. Substitute $R = 20$ ft and $r = 17$ ft. Then $A=\pi(20^{2}-17^{2})=\pi(400 - 289)=\pi\times111\approx3.14\times111 = 348.54$ square feet.

Step3: Calculate the total cost

The cost per square foot is $\$1.66$. So the total cost $C=1.66\times A$. Substitute $A = 348.54$ square feet. Then $C=1.66\times348.54\approx578.58$.

for the second question:

Step1: Recall the ratio of a golden rectangle

The ratio of the length to the width in a golden rectangle is $\frac{a}{b}=\frac{1 + \sqrt{5}}{2}\approx1.618$, where $a$ is the longer side and $b$ is the shorter side.

Step2: Solve for the shorter side

We know $a = 11$ inches. From $\frac{a}{b}=1.618$, we can solve for $b$ as $b=\frac{a}{1.618}$. Substitute $a = 11$ inches, then $b=\frac{11}{1.618}\approx6.8$ inches.

Answer:

The closest answer to $578.58$ is $\$578.87$. So the answer is $\$578.87$.