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.]

Verified step by step guidance

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.

Recommended video:

Guided course

01:56

Conversion Factors

Related Practice

Textbook Question

Two spheres of equal volume are placed on the scales as shown. a. Which one is more dense?

Textbook Question

Water has a density of 0.997 g/cm³ at 25 °C; ice has a density of 0.917 g/cm³ at -10 °C. (a) If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 °C, what volume does the ice occupy? (b) Can the ice be contained within the bottle?

Textbook Question

A 32.65-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 mL. The solid and toluene together weigh 58.58 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?

views

Textbook Question

Saline solution used in hospital contains 0.9% sodium chloride by mass. Calculate the number of grams of sodium chloride in 0.5 gal of saline solution if the solution has a density of 1.01 g/mL.

views

Textbook Question

A 40-lb container of peat moss measures 14 * 20 * 30 in. A40-lb container of topsoil has a volume of 1.9 gal. (b) How many bags of peat moss are needed tocover an area measuring 15.0 ft * 20.0 ft to a depth of 3.0 in.?

views