Question

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 of surface area approximately how much will it cost for the concrete?

Answer 1

Let's begin by identifying key information given to us:

diameter (D) = 18 ft = radius (r) = D/2 = 18/2 = 9

The area of the pool is given by:

`\begin{gathered} A_(pool)=\pi r^2_(pool) \\ \pi=3.14,r_(pool)=9ft \\ A_(pool)=3.14(9^2) \\ A_(pool)=254.34ft^2 \end{gathered}`

The radius of the pool with concrete is given as:

`\begin{gathered} r_(concrete)=9+4=13ft \\ r_(concrete)=13ft \end{gathered}`

As such, the area of the pool with concrete is given by:

`\begin{gathered} A_((pool+concrete))=\pi r_(concrete) \\ \pi=3.14,r_((pool+concrete))=13ft \\ A_((pool+concrete))=3.14(13^2) \\ A_((pool+concrete))=530.66ft^2 \end{gathered}`

The surface area of the concrete is calculated by the difference between the area of the pool with concrete & the area of the pool

`\begin{gathered} A_(concrete)=A_((pool+concrete))-A_(pool) \\ A_(concrete)=530.66-254.34 \\ A_(concrete)=276.32ft \end{gathered}`

A square foot cost $4.25. For 276.32 square feet, we will have:

`\begin{gathered} 276.32*4.25 \\ \Rightarrow1174.36 \\ \Rightarrow\text{\$}1,174.36 \end{gathered}`

Therefore, the concrete will cost about $1,174.36