Question

Zofia has a box shaped pool. its width is triple its depth and its length is double its width the floor of the pool measure exactly 761.76 square feet. find the volume of the poolI need help please help me

Answer 1

The pool is a box shape with width, length and depth. The volumen of the pool is:

$\text{Volumen}=\text{width}\cdot\text{length}\cdot\text{depth}$

And the area is 761.76 square feet:

$\text{Area}=\text{width}\cdot\text{length}=761.76ft^2$

We also know the width is triple of depth and length is double of width, so:

$\begin{gathered} length=2\cdot\text{width} \\ \text{width}=3\cdot\text{depth}\Rightarrow\text{length}=2\cdot3\cdot\text{depth}=6\cdot\text{depth} \\ \text{Area}=761.76ft^2=width\cdot length=3\cdot depth\cdot6depth \\ 761.76=18\cdot depth^2 \\ depth^2=\frac{761.76}{18}=42.32\Rightarrow depth=\sqrt[]{42.32}\approx6.5\text{ ft} \end{gathered}$

Now, we know the value of depth, so the width and length too.

So, we calculate the volumen:

$\begin{gathered} \text{depth}=6.5ft \\ \text{width}=3\cdot\text{depth}=3\cdot6.5ft=19.5ft \\ \text{length}=2\cdot\text{width}=2\cdot19.5ft=39ft \\ \text{Volumen}=\text{width}\cdot\text{length}\cdot\text{depth}=19.5\cdot39\cdot6.5=4943.25ft^3 \end{gathered}$

The Volumen is 4943.25 cubic feet