A swimming pool can be modeled by the following composite solid.
The solid consists of two smaller ones.
Top Prism: A rectangular prism with a length of l= 20 feet, a width of w= 15 feet, and a height of h= 3 feet.
Bottom Prism: A quadrangular prism with a trapezoidal base and a height of h=15 feet.
We are asked to find the volume of water that it takes to fill the pool. First we will find the volumes of each smaller solid. Then we will add the volumes.
Top Prism
Let's analyze the top prism.
The volume of a rectangular prism is the product of its dimensions.
\begin{gathered}
V_\text{top}={\color{#0000FF}{\ell}}\cdot{\color{#009600}{w}}\cdot{\color{#FF0000}{h}}={\color{#0000FF}{20}}\cdot {\color{#009600}{15}}\cdot {\color{#FF0000}{3}}=900
\end{gathered}
This tells us that the volume of the top prism is 900 cubic feet.
Bottom Prism
Now, let's analyze the bottom prism.
The base is a trapezoid with bases b_1= 10 and b_2= 20 feet, and a height h= 3 feet. Now, let's use the formula for the area of a trapezoid.
Therefore, the area of the base of Bottom Prism is B=45 square feet. Recall that the height of this prism is h=15 feet. Now, let's use the formula for the volume of a prism.
This tells us that the volume of the bottom prism is 675 cubic feet.
Volume of Pool
The volume of the top prism is \textcolor{darkorange}{V_\text{top}}=\textcolor{darkorange}{900} cubic feet, and the volume of the bottom prism is \textcolor{darkviolet}{V_\text{bottom}}=\textcolor{darkviolet}{675} cubic feet. Finally we will find the volume of the composite solid, which is equal to the volume of the pool.
