Let's break down the problem step by step based on the image.

Given:

• Dimensions of the pool: $15.0 \, \text{m} \times 6.0 \, \text{m}$
• Depth of water: $180 \, \text{cm} = 1.80 \, \text{m}$
• Density of water: $1000 \, \text{kg/m}^3$

Find:

1. The volume of water in the pool (in cubic meters).
2. The mass of the water in the pool (in kilograms).

Solution:

1. Volume of the water in the pool:

   • The volume of a rectangular pool is calculated by multiplying its length, width, and depth. $\text{Volume} = \text{Length} \times \text{Width} \times \text{Depth}$ Substituting the given values: $\text{Volume} = 15.0 \, \text{m} \times 6.0 \, \text{m} \times 1.80 \, \text{m} = 162 \, \text{m}^3$

2. Mass of the water in the pool:

   • The mass of water can be calculated using the formula: $\text{Mass} = \text{Density} \times \text{Volume}$ Substituting the known values: $\text{Mass} = 1000 \, \text{kg/m}^3 \times 162 \, \text{m}^3 = 162,000 \, \text{kg}$

Thus:

• Volume of water in the pool = $162 \, \text{m}^3$
• Mass of the water = $162,000 \, \text{kg}$

Would you like more details on any part of the solution?

Related Questions:

1. What is the weight of the water in Newtons if the acceleration due to gravity is $9.81 \, \text{m/s}^2$?
2. How would the volume change if the depth of the pool is increased by 20 cm?
3. What is the density of seawater, and how would that affect the mass calculation?
4. How would you calculate the volume of water if the pool was filled only halfway?
5. If the pool was circular instead of rectangular, how would you calculate the volume?

Tip:

Always make sure to convert all measurements to consistent units before performing any calculations to avoid errors.