The formula for density is given by [tex]p=\frac{M}{V}[/tex], where [tex]p[/tex] is density, [tex]M[/tex] is mass and [tex]V[/tex] is volume. If a substance has a mass of 27.82 grams and a volume of 3.6 ml, what is the most accurate density?
Answer (2)
Calculate the density using the formula p = V M , where M = 27.82 grams and V = 3.6 ml.
The calculated density is approximately 7.7278.
Compare the calculated density with the given options (7.7, 7.7278, 7.73, 0.1) to find the closest value.
The most accurate density is 7.7278 .
Explanation
Understanding the Problem We are given the formula for density: p = V M , where p is density, M is mass, and V is volume. We are given that the mass M = 27.82 grams and the volume V = 3.6 ml. Our objective is to find the most accurate density from the given options: 7.7, 7.7278, 7.73, and 0.1.
Calculating the Density First, we calculate the density using the given mass and volume: p = 3.6 27.82 .
Comparing with Given Values The result of the calculation is approximately 7.727777777777778. Now, we compare this calculated density to the four possible values to find the closest one.
Finding the Closest Value Comparing the calculated density (approximately 7.7278) with the given options:
7.7 is different by |7.7278 - 7.7| = 0.0278
7.7278 is different by |7.7278 - 7.7278| = 0
7.73 is different by |7.7278 - 7.73| = 0.0022
0.1 is different by |7.7278 - 0.1| = 7.6278
The value 7.7278 is the closest to the calculated density.
Conclusion Therefore, the most accurate density from the given options is 7.7278.
Examples
Density calculations are crucial in many real-world applications. For instance, in material science, knowing the density of a substance helps in identifying it and predicting its behavior under different conditions. In the food industry, density measurements are used to ensure the quality and consistency of products. Understanding density also plays a vital role in designing ships and submarines, where buoyancy and stability depend on accurate density calculations. This concept is also used in geology to study the composition of the Earth's layers.
The density of a substance with a mass of 27.82 grams and a volume of 3.6 ml is calculated to be approximately 7.7278 grams per ml. The most accurate density from the given options is therefore 7.7278. This value is found by using the formula for density, which is mass divided by volume.
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