Acircular pool with a diameter of 18 ft will have a uniform 4 ft concrete walkway poured around it. if the concrete cost

A circular pool with a diameter of 18 ft will have a uniform 4 ft concrete walkway poured around it. If the concrete cost $4.25 a square foot, how much will it cost for the concrete?

This can be solve be solving the area of walkway

Area of walkway is equal to = (pi)( 9 ft +4) ^2– (pi)(9ft)^2

= 276.46 sq ft

Cost = 276.46 sq ft * ($4.25 a square foot) = $1174.70

$1,174.70

Step-by-step explanation:

Given : A circular pool with a diameter of 18 ft will have a uniform 4 ft concrete walkway poured around it.

To Find: If the concrete cost $4.25 a square foot, how much will it cost for the concrete?

Solution:

A circular pool has  diameter of 18 ft will have a uniform 4 ft concrete walkway   around it.

So radius = diameter /2 =18/2 =9 feet

Thus Area of circular pool = [tex]\pi r^{2}[/tex] = [tex]\pi 9^{2}[/tex]

Use π =3.14

  Thus Area of circular pool =  [tex]3.14*9^{2}[/tex]

                                             =  [tex]3.14*81[/tex]

                                             =  254 . 37 square feet

Since the Radius of the pool with concrete = 9 + 4= 13

So, Area of circular pool with concrete=   [tex]3.14*13^{2}[/tex]

                                             =  [tex]3.14*169[/tex]

                                             =  530.66 square feet

Now surface area of concrete = area of pool with concrete - area of pool

Surface area of concrete= 530.66 - 254.34 = 276.32 square feet

If the concrete cost $4.25 a square foot of surface area,

So the cost for the concrete of  276.32 square feet  =  276.32 * 4.25 = $ 1174.36

The option close to our answer is $1,174.70

Thus Option D is correct

Below is the solution:

volume = lwh 
= 18(3)(1/3) 
= 18 cubic feet

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Diameter = 18 ft.
Radius = 18/2 = 9 ft.

Area for walkway around the circular pool =
Area of R (R = 9+4 ft.) - Area of Pool (r = 9 ft.)

πR² - πr²
π(R²-r²)
π(13²-9²)
π(169-81)
π(88)

Now,
1 sq. foot = $ 4.25
π(88) sq. foot = [tex]\frac{22}{7} \times 88 \times 4.25 = 1175.42[/tex]

So, Answer will be B. $1174.70 because of the closeness to our answer.

If you visualize the problem, there are two concentric circles, the pool, and the pool plus the walkway. So, we have to subtract the area of these two concentric circles to find the walkway.

Bigger circle: Pool plus walkway

diameter = 18 + 4(2)   -- this is because there is 2 ft of walkway at each far end
diameter = 26 ft
Area = pi*(26/2)^2
Area = 530.93 ft2

Smaller circle:pool

diameter = 18 ft
Area = pi*(8/2)^2
Area = 50.27 ft2

Area of walkway

A = 530.93 - 50.27
A = 480.66 ft2

Then the cost would be
Cost = $4.25 * 480.66
Cost = $2,042.81

The answer to your question is B