Calculate the mass of each of the following: (a) a sphere of...

Calculate the mass of each of the following: (a) a sphere of gold with a radius of $10.0 \mathrm{cm}$ (volume of a sphere with a radius $r$ is $V=4 / 3 \pi r^{3} ;$ density of gold $=19.3 \mathrm{g} / \mathrm{cm}^{3},$ (b) a cube of platinum of edge length $\left.0.040 \mathrm{mm} \text { (density }=21.4 \mathrm{g} / \mathrm{cm}^{3}\right),(\mathrm{c}) 50.0 \mathrm{mL}$ of ethanol (density $=0.798 \mathrm{g} / \mathrm{mL}$ ).

Calculate the mass of each of the following: (a) a sphere of gold with a radius of $10.0 \mathrm{cm}$ (volume of a sphere with a radius $r$ is $V=4 / 3 \pi r^{3} ;$ density of gold $=19.3 \mathrm{g} / \mathrm{cm}^{3},$ (b) a cube of platinum of edge length $\left.0.040 \mathrm{mm} \text { (density }=21.4 \mathrm{g} / \mathrm{cm}^{3}\right),(\mathrm{c}) 50.0 \mathrm{mL}$ of
ethanol (density $=0.798 \mathrm{g} / \mathrm{mL}$ ).

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Key Concepts

Density

Density is a measure of mass per unit volume and is a key property of substances that allows you to calculate the mass of an object if its volume is known. It is typically expressed in units such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³), and the relationship is given by the formula mass = density × volume.

Volume Calculation of Three-Dimensional Objects

Volume calculation involves determining the space occupied by a three-dimensional object. Standard formulas exist for different shapes, such as V = (4/3)?r³ for a sphere and V = edge³ for a cube. These formulas are essential for converting geometric dimensions into volume measurements, which can then be used with density to determine mass.

Unit Conversion

Unit conversion is an essential process in problem solving that ensures all measurements are in compatible units before any calculations are performed. In scenarios where dimensions and densities are provided in different units, converting units (for example, from millimeters to centimeters) is critical to ensure accuracy in volume and mass calculations.

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