Math Problem Statement
Solution
The problem in the image asks for the volume of water needed to fill a swimming pool and how many kilograms of seawater would be required based on the given density. Let's break down the problem:
Information given:
- Density of seawater:
- Pool dimensions:
- Depth:
- Width:
- Length:
a) Volume of water the pool can hold:
The volume of a rectangular pool is calculated by multiplying its dimensions: Substituting the values: So, the volume of water required to fill the pool is 750 cubic meters.
b) Kilograms of seawater needed:
We need to convert the volume from cubic meters to cubic centimeters to use the density given in .
So:
Now, using the density of seawater (), we can find the mass: Since , we convert to kilograms:
Thus, 780,000 kilograms of seawater are needed to fill the pool.
Would you like more details on any step or have further questions?
Here are 5 related questions to think about:
- How would the volume change if the pool depth were doubled?
- What is the total weight of seawater in pounds instead of kilograms?
- If the pool had an irregular shape, how would you calculate the volume?
- What would happen to the required mass if the density of the water changed to ?
- How would evaporation affect the amount of water required to keep the pool full?
Tip: Always remember to keep track of unit conversions, especially when working with densities and volumes!
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Math Problem Analysis
Mathematical Concepts
Volume Calculation
Unit Conversion
Density and Mass Relationship
Formulas
Volume of a rectangular pool: V = length × width × depth
Mass = Density × Volume
1 m³ = 1,000,000 cm³
Theorems
-
Suitable Grade Level
Grades 9-12
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