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Question: The mass of a diamond is \( 1.76g \) . The volume is \( 0.5c{m^3} \) . What is the density of the di...

The mass of a diamond is 1.76g1.76g . The volume is 0.5cm30.5c{m^3} . What is the density of the diamond?

Explanation

Solution

The density of a substance (more precisely, volumetric mass density; also called specific mass) is its mass per unit volume. The most commonly used symbol for density is ρ\rho (lowercase Greek letter rho), although the letter D can also be used. The density of a given material shows its density in a specific area. It is usually a measure of how closely the matter particles are packed together. In the solution, we will use its mass and volume to calculate the density of the diamond.

Complete answer:
As we know, the term "density" refers to a measure of the mass of an object or an object with a volume unit. It is represented by the symbol ρ\rho , or simply by the letter D. Quantitatively speaking, density is mass divided by volume. The density of a given material basically shows its density in a specific area. It is usually used to measure the tightness of material particles.
The Greek scientist Archimedes discovered the principle of density. The density of an object indicates its weight in a constant volume. Mathematically, the density of an object can be calculated with the help of the following formula:
Density=massvolumeDensity = \dfrac{{mass}}{{volume}}
Volume of the diamond is 0.5cm30.5c{m^3} and the mass of the diamond is 1.76g1.76g . Now, substitute these values in the formula of calculating density given above:
Density=1.76g0.5cm3Density = \dfrac{{1.76g}}{{0.5c{m^3}}}
Density=3.52gcm−3Density = 3.52gc{m^{ - 3}}
Therefore, the density of diamond is found to be 3.52gcm−3.3.52gc{m^{ - 3}}.

Note:
We must keep in mind that density plays a vital role in many applications. The lifeguard tubes we find in beaches or swimming pools are designed to float in water so that people can swim without sinking, just fill these tubes up Air. The lifeguard tube is filled with air less dense than water, so it is always floating. Another application is that ships can float because they have air-filled ballast tanks. These ballast tanks are bulky and light, which reduces the density of the ship. Combined with buoyancy, this reduced density helps the boat float on the water.