A liquid that occupies a volume of 4.7 L has a mass of 5.1 kg. What is the density of the liquid in [tex]$kg / L$[/tex]? density = [ ? ] kg/L. Round your answer to the tenths place.
Answer (2)
Calculate the density using the formula: d e n s i t y = v o l u m e ma ss .
Substitute the given values: d e n s i t y = 4.7 L 5.1 k g .
Perform the calculation: d e n s i t y ≈ 1.0851 k g / L .
Round the result to the tenths place: d e n s i t y ≈ 1.1 k g / L .
Explanation
Understanding the Problem We are given the mass and volume of a liquid and asked to find its density. Density is defined as mass per unit volume.
Stating the Formula and Given Values The formula for density is: d e n s i t y = v o l u m e ma ss We are given: Mass = 5.1 kg Volume = 4.7 L
Calculating the Density Now, we plug in the given values into the formula: d e n s i t y = 4.7 L 5.1 kg Performing the division, we get: d e n s i t y ≈ 1.0851 kg/L We are asked to round the answer to the tenths place, so we round 1.0851 to 1.1.
Final Answer Therefore, the density of the liquid is approximately 1.1 kg/L.
Examples
Understanding density is crucial in many real-world applications. For instance, when designing ships, engineers need to calculate the density of materials to ensure the ship floats. Similarly, in cooking, knowing the density of ingredients helps in measuring quantities accurately. In geology, density helps in identifying different types of rocks and minerals. Density is also used in determining the purity of substances, such as gold. For example, if you have a gold nugget with a volume of 10 c m 3 and a mass of 193 g , its density would be 10 c m 3 193 g = 19.3 g / c m 3 , which is the density of pure gold.
The density of the liquid is calculated using the formula density = mass/volume. Given that the mass is 5.1 kg and the volume is 4.7 L, the density calculates to approximately 1.1 kg/L when rounded to the tenths place. This value indicates the mass of the liquid per liter of volume.
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