Question

Jeanine’s swimming pool has a diameter of 27 feet. Surrounding the pool is a deck that extends 5 feet from the edges of the pool. Jeanine wants to paint the deck and then put a fence around it. Paint costs $0.85 per square foot and fencing costs $8.25 per foot. How much will it cost Jeanine to paint the deck and add fencing?

Answer 1

The total cost of painting the deck and add fencing is $1,386.79.

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

`=\pi R^(2)-\pi r^(2)\\\\=\pi(R^(2)-r^(2))\\\\=(22)/(7)* [((37)/(2))^(2)-((27)/(2))^(2)]\\\\=502.86`

Then the cost of painting the deck is:

Cost of painting = Area of Deck × Cost of paint/square foot

`=502.86* \$0.85\\=\$427.431\\\approx \$427.43`

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

`=2\pi R* \$8.25\\\\=2* (22)/(7)* (37)/(2)* \$8.25\\\\=\$959.36`

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.