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When dealing with cylindrical objects in chemistry or physics, calculating the volume is often the first step. A cylindrical object, like a glass of water, has a specific shape that requires a formula for accurate volume measurement. The formula for the volume of a cylinder is given by:

• \[ V = \pi r^2 h \]

Here, \( r \) is the radius of the cylinder's base, and \( h \) is the height of the cylinder.
The radius and height must be in the same units for consistency; in this problem, they are both provided in centimeters (cm).
To find the volume, you simply plug the numbers into the formula and compute:

• The radius \( r = 4.50 \) cm
• Height \( h = 12.0 \) cm

So the volume, \( V \), becomes:

• \[ V = \pi (4.50)^2 (12.0) \approx 763.41 \ ext{cm}^3 \]

This result indicates the total space occupied by the water in cubic centimeters. Understanding this concept allows us to bridge into density and mass conversion.

Once you have the volume, the next step involves using the concept of density to find the mass of the substance contained in that volume. Density is a measure of how much mass is contained within a given volume. It is given by the formula:

• \[ ext{Density} = \frac{\text{Mass}}{\text{Volume}} \]

In the problem, the density of water is provided as \( 1.00 \, \text{g/cm}^3 \). This means that every cubic centimeter of water weighs 1 gram. By rearranging the formula, you can find the mass:

• \[ \text{Mass} = \text{Density} \times \text{Volume} \]

We previously calculated the volume as \( 763.41 \ ext{cm}^3 \), which directly leads to the mass calculation:

• \[ \text{Mass} = 1.00 \times 763.41 = 763.41 \, \text{g} \]

Mass and density conversions become essential when moving on to find the chemical properties and molarity of the substances involved.

Finally, with the mass known, the number of moles of the substance can be calculated. Moles describe the amount of substance and are an essential concept in chemistry. To find moles, you use the molar mass, which is specific to each substance. For water \( \text{H}_2\text{O} \), the molar mass is \( 18.02 \ ext{g/mol} \). The formula connecting mass to moles is:

• \[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]

Substituting the values:

• \[ \text{Moles} = \frac{763.41}{18.02} \approx 42.37 \ ext{moles} \]

This calculation shows how many moles, or in simpler terms, how many times the basic formula unit of water is present in the glass. Understanding moles is crucial for stoichiometry and predicting the outcomes of chemical reactions.