A sample of aluminum has a volume of 23cm^3 The density of aluminum is 2.7 g/cm^3 Calculate the mass of the same using dimensional analysis.Make sure to show your work.

To calculate the mass of the aluminum sample using dimensional analysis, we use the formula for density:<br /><br />\[<br />\text{Density} = \frac{\text{Mass}}{\text{Volume}}<br />\]<br /><br />Rearranging this formula to solve for mass:<br /><br />\[<br />\text{Mass} = \text{Density} \times \text{Volume}<br />\]<br /><br />### Given:<br />- Volume (\(V\)) = \(23 \, \text{cm}^3\)<br />- Density (\(\rho\)) = \(2.7 \, \text{g/cm}^3\)<br /><br />### Step-by-Step Solution:<br /><br />1. Write the formula for mass:<br /> \[<br /> \text{Mass} = \text{Density} \times \text{Volume}<br /> \]<br /><br />2. Substitute the given values into the formula:<br /> \[<br /> \text{Mass} = 2.7 \, \text{g/cm}^3 \times 23 \, \text{cm}^3<br /> \]<br /><br />3. Perform the multiplication:<br /> \[<br /> \text{Mass} = 62.1 \, \text{g}<br /> \]<br /><br />4. Check units:<br /> - The unit \(\text{cm}^3\) in the numerator (from volume) cancels with \(\text{cm}^3\) in the denominator (from density), leaving the unit as grams (\(\text{g}\)), which is correct for mass.<br /><br />### Final Answer:<br />The mass of the aluminum sample is:<br /><br />\[<br />\boxed{62.1 \, \text{g}}<br />\]