Volume to Mass Conversion Problem

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SUMMARY

The discussion centers on calculating the volume and mass of water needed to fill a cylindrical swimming pool with a height of 132 cm and a diameter of 365 cm. The volume is determined using the formula for the volume of a cylinder, V = πr²h, where r is the radius and h is the height. Given that 1 cubic decimeter equals 1 liter, the volume in liters can be directly derived from the cubic centimeters. The mass of the water can then be calculated using the density of water, which is 1.0 g/cm³, confirming that the mass in grams will equal the volume in cubic centimeters.

PREREQUISITES
  • Understanding of the formula for the volume of a cylinder (V = πr²h)
  • Knowledge of unit conversions between cubic centimeters and liters
  • Familiarity with the concept of density (mass/volume)
  • Basic mathematical skills for calculations involving π and unit conversions
NEXT STEPS
  • Research the formula for the volume of different geometric shapes
  • Learn about unit conversions between metric measurements
  • Study the relationship between mass, volume, and density in various materials
  • Explore practical applications of volume and mass calculations in real-world scenarios
USEFUL FOR

Students in physics or mathematics courses, educators teaching geometry or measurement concepts, and anyone needing to understand volume and mass calculations in practical applications.

Amil
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My first week of class and I'm just tied up with this problem. I must be missing something.
Question:
A cylindrical swimming pool is 132 cm high and 365 cm in diameter. What will be the volume (in liters) of water necessary to fill this pool, knowing that one cubic decimeter is equal to one liter? Supposing that the desity of water is 1.0g/cm3, what will be the mass of water in this pool?

Thanks in advance for any help. I really need to understand how to convert thse types of units.

AMIL
 
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What is the formula for finding the volume of a cylinder?

What is the relationship between mass, volume and density?

You should be able to find these formula in your book, let the units be your guide.
 
Even without formulas, you should be able to reason through this. You know that a cylinder has a circular base and top. Think about what the volume is: the cylinder is basically a pile of circles on tom of each other that add up to a lenth (the side length of the cylinder). I dunno, this might be confusing, but whenever you can, try not to use formulas without understanding what they mean and where they come from. Same for the density part.
 

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