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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?

A$1,714.07
B$1,247.08
C$276.40
D$1,174.70

Verified Answer :

MissPhiladelphia

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

Answer:

$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 = \(\pi r^{2}\) = \(\pi 9^{2}\)

Use π =3.14

  Thus Area of circular pool =  \(3.14*9^{2}\)

                                             =  \(3.14*81\)

                                             =  254 . 37 square feet

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

So, Area of circular pool with concrete=   \(3.14*13^{2}\)

                                             =  \(3.14*169\)

                                             =  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