A cicular pool with a radius oF 12 meter if filled with water to a depth of 3 meters. What is the weight of water in the swimming pool?
the volume of water is
... π * 12^2 * 3 m^3
a cubic meter (m^3) of water has a mass of 1000 kg (a metric ton)
the weight is the mass multiplied by the gravitational acceleration
... g = 9.8 m/s^2
the weight is in Newtons -- a unit of force
To determine the weight of water in the swimming pool, we need to know the density of water and the volume of water in the pool.
1. Density of water: The density of water is approximately 1000 kilograms per cubic meter (kg/m³).
2. Volume of water: The volume of a swimming pool can be calculated using the formula for the volume of a cylinder: V = π * r² * h, where V is the volume, π is a constant (approximately 3.14159), r is the radius of the pool, and h is the height or depth of the water.
In this case, the radius of the circular pool is 12 meters, and the water is filled to a depth of 3 meters.
Substituting the values into the formula, we have: V = 3.14159 * (12^2) * 3
Calculating that gives us: V ≈ 3.14159 * 144 * 3 ≈ 1357.1684 cubic meters.
3. Weight of water: We can calculate the weight of water by multiplying the volume of water by the density of water.
Using the density of water (1000 kg/m³) and the volume we calculated (1357.1684 cubic meters), we get:
Weight = Volume * Density = 1357.1684 * 1000 ≈ 1,357,168.4 kilograms.
Therefore, the weight of water in the swimming pool is approximately 1,357,168.4 kilograms.