Final answer:
To find the volume of a gold medal with a diameter of 60 mm and a thickness of 3 mm, the formula for the volume of a cylinder is used, and then multiplied by the density of gold to get the mass.
Step-by-step explanation:
The volume of a gold medal can be calculated using the formula for the volume of a cylinder, which is V = πr²h. Given that the diameter (d) is 60 mm (which means the radius r is 30 mm, or 3 cm), and the thickness (h) is 3 mm (or 0.3 cm), the volume in cubic centimeters would be π(3 cm)²(0.3 cm). To convert the volume into a mass, we use the density (d) of gold, which is 19 g/cm³.
First, calculate the volume:
V = π(3 cm)²(0.3 cm) = π(9 cm²)(0.3 cm) = π(2.7 cm³) = 8.4823 cm³ (approximately).
Then, using the density to find the mass, we have:
mass = volume × density = 8.4823 cm³ × 19 g/cm³ = 161.16 grams (approximately).
The mass provides a quantitative measurement of the gold medal's volume in grams, making it possible to understand how much space the medal occupies based on its density.