Volume to Mass Conversion Problem

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To find the volume of a cylindrical swimming pool measuring 132 cm in height and 365 cm in diameter, the formula for the volume of a cylinder (V = πr²h) should be applied, where r is the radius. The volume calculated in cubic centimeters can then be converted to liters, as 1 cubic decimeter equals 1 liter. Understanding the relationship between mass, volume, and density is crucial, with the density of water being 1.0 g/cm³, which means the mass can be derived directly from the volume. It's important to grasp the concepts behind the formulas rather than just memorizing them for better comprehension. Mastering these conversions will enhance problem-solving skills in future 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?

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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