Respuesta :
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:
[tex]\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}[/tex]The radius of the pool with concrete is given as:
[tex]\begin{gathered} r_{concrete}=9+4=13ft \\ r_{concrete}=13ft \end{gathered}[/tex]As such, the area of the pool with concrete is given by:
[tex]\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}[/tex]The surface area of the concrete is calculated by the difference between the area of the pool with concrete & the area of the pool
[tex]\begin{gathered} A_{concrete}=A_{(pool+concrete)}-A_{pool} \\ A_{concrete}=530.66-254.34 \\ A_{concrete}=276.32ft \end{gathered}[/tex]A square foot cost $4.25. For 276.32 square feet, we will have:
[tex]\begin{gathered} 276.32\times4.25 \\ \Rightarrow1174.36 \\ \Rightarrow\text{\$}1,174.36 \end{gathered}[/tex]Therefore, the concrete will cost about $1,174.36
