Question

the swimming pool at the right is being filled with water.Find the number of cubic feet that it will take to fill the swimming pool

Answer 1

`2400ft^3`

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:

`V_1=l*w*h\\\\Where:\\\\l=Length\\w=Width\\h=Height`

And the volume of the trapezoidal prism is given by:

`V_2=l*((1)/(2) *(a+b)*h)\\\\Where:\\\\a=Short\hspace{3}base\\b=Long\hspace{3}base\\h=Height\\l=Length`

Therefore, the volumen of the swimming pool will be given by:

`V_p=V_1+V_2`

Hence, let's find the volume of the rectangular prism:

For the rectangular prism:

`w=14ft\\h=8ft\\l=12ft`

So:

`V_1=(14)*(8)*(12)=1344ft^3`

Now, let's find the volume of the trapezoidal prism:

For the trapezoidal prism:

`a=3ft\\b=8ft\\h=16ft\\l=12ft`

So:

`V_2=(12)*((1)/(2) *(3+8)*16)=1056ft^3`

Thus, the volume of the swimming pool is:

`V_p=1344ft^3+1056ft^3=2400ft^3`

Therefore the number of cubic feet required to fill the swimming pool is
`2400ft^3`

Answer 2

The volume of the swimming pool when filled with water will be given by:
Volume=(L×W×H)+(1/2*B×H×L)+(L×W×H)
V=(14×12×8)+(1/2×16×8×12)+(5×16×12)
V=1344+768+960
V=3072 ft³

Thus the volume of water required will be 3072 ft³