PLEASE HELP Unit conversion (Volume, Mass, Density)

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SUMMARY

The discussion centers on calculating the volume and mass of water required to fill a cylindrical swimming pool with a height of 132 cm and a diameter of 365 cm. The volume is calculated using the formula for the volume of a cylinder, resulting in 13,804,774.5 cm³, which converts to 13,804.77 liters since 1,000 cm³ equals 1 liter. The mass of the water, given the density of water at 1.0 g/cm³, is numerically identical to the volume in grams, confirming that the mass is also 13,804.77 grams.

PREREQUISITES
  • Understanding of basic geometry, specifically the formula for the volume of a cylinder.
  • Knowledge of unit conversion between cubic centimeters and liters.
  • Familiarity with density concepts, particularly the density of water.
  • Basic arithmetic skills for calculations involving volume and mass.
NEXT STEPS
  • Learn about the formula for the volume of different geometric shapes, including spheres and cones.
  • Research unit conversion techniques for various measurement systems.
  • Explore density calculations for different substances beyond water.
  • Practice solving real-world problems involving volume and mass in various contexts.
USEFUL FOR

Students in introductory physics or chemistry courses, educators teaching unit conversion and density, and anyone needing to apply geometric formulas in practical scenarios.

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?

I calculated that the cylinder has a volume of 1.380 x 10^7 cm^3 (13804774.5 cm^2) using the pi x r^2 x h formula. But what next?

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

AMIL
 
Mathematics news on Phys.org
1000 cubic cm = 1 liter, so your volume is 1.380 x 104 liters. Mass in grams = volume in cubic cm.
 
mathman said:
Mass in grams = volume in cubic cm.
More generally, mass = density * volume.

In the case of water, when mass is in grams and volume is in cm^3, the mass and volume are numerically identical, because water has a density of one gram per cubic centimeter. In general, however, you have to be careful.

- Warren
 

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