A thief plans to steal a cylindrical platinum medal with a radius of 2.3 cm and a thickness of 0.8 cm from a jewellery store. If the platinum has a density of 21.45 g/cm³, what is the mass of the medal in kg? [The volume of a cylinder is V = πr²h.]

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

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Calculate the volume of the cylindrical medal using the formula for the volume of a cylinder: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the thickness.

Substitute the given values into the volume formula: \( r = 2.3 \text{ cm} \) and \( h = 0.8 \text{ cm} \).

Compute the volume \( V \) in cubic centimeters (cm³) using the substituted values.

Use the density formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \) to find the mass. Rearrange it to \( \text{Mass} = \text{Density} \times \text{Volume} \).

Substitute the calculated volume and the given density (21.45 g/cm³) into the mass formula to find the mass in grams, then convert the mass from grams to kilograms by dividing by 1000.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or thickness). This formula derives from the area of the circular base (πr²) multiplied by the height, providing a measure of the three-dimensional space the cylinder occupies.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It indicates how much mass is contained in a given volume of a substance. In this case, the density of platinum is crucial for converting the calculated volume of the medal into mass.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this problem, after calculating the mass of the platinum medal in grams, it is necessary to convert this value to kilograms, as 1 kg equals 1000 g. This step ensures that the final answer is in the desired unit of measurement.

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