Use the mass and volume data to calculate the density of an unknown metal to the nearest hundredth.
Mass of unknown metal = [tex]$222.50 g$[/tex]
Volume of unknown metal = [tex]$25.00 cm^3$[/tex]
Answer (1)
Calculate the density using the formula: De n s i t y = V o l u m e M a ss .
Substitute the given values: De n s i t y = 25.00 c m 3 222.50 g .
Perform the division: De n s i t y = 8.9 g / c m 3 .
Round the result to the nearest hundredth: De n s i t y = 8.90 g / c m 3 . The density of the unknown metal is 8.90 g / c m 3 .
Explanation
Understanding the Problem We are given the mass and volume of an unknown metal and asked to calculate its density to the nearest hundredth. Density is defined as mass per unit volume.
Stating the Formula and Given Values The formula for density is: De n s i t y = V o l u m e M a ss We are given: Mass = 222.50 g Volume = 25.00 c m 3
Calculating the Density Now, we substitute the given values into the formula: De n s i t y = 25.00 c m 3 222.50 g Performing the division, we get: De n s i t y = 8.9 g / c m 3
Rounding to the Nearest Hundredth Since we need to round the result to the nearest hundredth, we can write 8.9 as 8.90 .
Therefore, the density of the unknown metal is 8.90 g / c m 3 .
Examples
Understanding density is crucial in many real-world applications. For example, when designing ships, engineers need to calculate the density of the materials used to ensure the ship floats. Similarly, in construction, knowing the density of concrete helps determine the structural integrity of buildings. In geology, density helps identify different types of rocks and minerals. Knowing how to calculate density allows us to predict how materials will behave under different conditions.
