To solve this problem, we calculate the volume of water needed in each case using the formula for the volume of a rectangular prism:

$\text{Volume} = \text{Length} \times \text{Width} \times \text{Depth}.$

The dimensions of the pool are:

• Length $L = 50 \, \text{m}$,
• Width $W = 20 \, \text{m}$,
• Depth $D = 2 \, \text{m}$.

a) The pool is filled to the level of the deck.

Here, the pool is completely filled, so the depth is the full $2 \, \text{m}$.

$\text{Volume} = 50 \times 20 \times 2 = 2000 \, \text{m}^3.$

b) The pool is filled to within 20 cm of the level of the deck.

Here, the pool is not filled completely. Since $20 \, \text{cm} = 0.2 \, \text{m}$, the depth becomes:

$\text{Depth} = 2 - 0.2 = 1.8 \, \text{m}.$

The volume is:

$\text{Volume} = 50 \times 20 \times 1.8 = 1800 \, \text{m}^3.$

c) The pool is half filled.

If the pool is half filled, the depth is:

$\text{Depth} = \frac{2}{2} = 1 \, \text{m}.$

The volume is:

$\text{Volume} = 50 \times 20 \times 1 = 1000 \, \text{m}^3.$

Final Answers:

1. (a) The pool is filled to the level of the deck: 2000 m³.
2. (b) The pool is filled to within 20 cm of the deck: 1800 m³.
3. (c) The pool is half filled: 1000 m³.

Let me know if you need further clarifications or explanations!

Related Questions:

1. How do you convert cubic meters to liters?
2. If the pool was 1 meter longer, how would the water volume change?
3. How much water is needed to raise the water level by 50 cm in a half-filled pool?
4. If the pool has a leak losing 10 m³ per hour, how long would it take to empty?
5. What is the surface area of the pool?

Tip: Always double-check your units, especially when converting between meters and centimeters!