Answer :
Answer:
The total cost of painting the deck and add fencing is $1,386.79.
Step-by-step explanation:
Consider the diagram below.
The smaller circle represents Jeanine’s swimming pool with diameter,
d = 27 feet.
And the outer circle represents the deck.
The width of the deck is 5 feet.
Then the diameter of the bigger circle is:
D = 27 + 5 + 5 = 37 feet
It is provided that Jeanine wants to paint the deck and the paint costs $0.85 per square foot.
The cost of painting the deck can be computed using the formula:
Cost of painting = Area of Deck × Cost of paint/square foot
Compute the area of the deck as follows:
Area of Deck = Area of bigger circle - Area of smaller circle
[tex]=\pi R^{2}-\pi r^{2}\\\\=\pi(R^{2}-r^{2})\\\\=\frac{22}{7}\times [(\frac{37}{2})^{2}-(\frac{27}{2})^{2}]\\\\=502.86[/tex]
Then the cost of painting the deck is:
Cost of painting = Area of Deck × Cost of paint/square foot
[tex]=502.86\times \$0.85\\=\$427.431\\\approx \$427.43[/tex]
The cost of painting the deck is $427.43.
Now Jeanine also wants to put a fence around the deck.
The cost of fencing is, $8.25 per foot.
The cost of putting the fence can be computed using the formula:
Cost of putting the fence = Circumference of the big circle × Cost of fencing
Compute the cost of putting the fence as follows:
Cost of putting the fence = Circumference of the big circle × Cost of fencing
[tex]=2\pi R\times \$8.25\\\\=2\times \frac{22}{7}\times \frac{37}{2}\times \$8.25\\\\=\$959.36[/tex]
The cost of putting the fence is $959.36.
The total cost of painting the deck and add fencing is:
Total Cost = Cost of painting the deck + Cost of putting the fence
= $427.43 + $959.36
= 1386.79
Thus, the total cost of painting the deck and add fencing is $1,386.79.
