Calculate Total Pool Volume: 180 m³ is 40% of What?

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information.
• Step 2: Use the appropriate formula to determine the total capacity of the pool.
• Step 3: Perform the necessary calculations to find the answer.

Now, let's work through each step:

Step 1: We are informed that 40% of the pool's capacity is filled with 180 $m^3$ of water.
This means that 40% of the pool's total capacity equals 180 $m^3$.

Step 2: To find the total capacity (denoted by $T$), use the percentage formula:
$T = \frac{\text{Percentage value}}{\left( \frac{\text{Percentage}}{100} \right)}$

Step 3: Substitute the known values into the formula:
$T = \frac{180}{\left( \frac{40}{100} \right)}$

This simplifies to:
$T = \frac{180}{0.4} = 450$

Therefore, the total capacity of the pool is 450 $m^3$.