Answer:
[tex]2400ft^3[/tex]
Step-by-step explanation:
This problem can be solve in many ways, however, I believe that the easiest way is the following:
First, take a look at the pictures that I attached you. As you can see I split the pool into two solids. A rectangular prism and a trapezoidal prism. The volume of the rectangular prism is given by:
[tex]V_1=l*w*h\\\\Where:\\\\l=Length\\w=Width\\h=Height[/tex]
And the volume of the trapezoidal prism is given by:
[tex]V_2=l*(\frac{1}{2} *(a+b)*h)\\\\Where:\\\\a=Short\hspace{3}base\\b=Long\hspace{3}base\\h=Height\\l=Length[/tex]
Therefore, the volumen of the swimming pool will be given by:
[tex]V_p=V_1+V_2[/tex]
Hence, let's find the volume of the rectangular prism:
For the rectangular prism:
[tex]w=14ft\\h=8ft\\l=12ft[/tex]
So:
[tex]V_1=(14)*(8)*(12)=1344ft^3[/tex]
Now, let's find the volume of the trapezoidal prism:
For the trapezoidal prism:
[tex]a=3ft\\b=8ft\\h=16ft\\l=12ft[/tex]
So:
[tex]V_2=(12)*(\frac{1}{2} *(3+8)*16)=1056ft^3[/tex]
Thus, the volume of the swimming pool is:
[tex]V_p=1344ft^3+1056ft^3=2400ft^3[/tex]
Therefore the number of cubic feet required to fill the swimming pool is [tex]2400ft^3[/tex]
