A thief plans to steal a cylindrical platinum medal with a...

A thief plans to steal a cylindrical platinum medal with a radius of $2.3 \mathrm{~cm}$ and a thickness of $0.8 \mathrm{~cm}$ from a jewellery store. If the platinum has a density of $21.45 \mathrm{~g} / \mathrm{cm}^{3},$ what is the mass of the medal in $\mathrm{kg} ?$ [The volume of a cylinder is $\left.V=\pi r^{2} h .\right]$

Key Concepts

Mass Calculation from Density and Volume

Once the volume of an object is known, the mass can be calculated by multiplying the volume by the density. This relationship, expressed by the formula mass = density × volume, is a key principle in physics and material science that links the physical dimensions of an object with its weight or mass.

Unit Conversion

Unit conversion is a critical skill in science that involves converting measurements from one unit to another to ensure consistency and accuracy. In the context of mass calculations, converting grams to kilograms (where 1 kg = 1000 g) is necessary when the final answer requires a different unit of measurement from that provided by the initial calculation.

Volume of a Cylinder

This concept involves calculating the space an object occupies when it has the shape of a cylinder. The formula V = ?r²h is used, where r represents the radius of the base and h represents the height (or thickness). Understanding this formula is fundamental to computing volumes for cylindrical objects in geometry.

Density

Density is defined as the mass per unit volume of a substance. It provides a relationship between the amount of matter in an object and the space it occupies. The density concept is crucial in various fields, including physics and engineering, as it helps in determining material properties and how different substances compare in terms of their compactness.

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