A round coin has a diameter of 19.55 mm , a thickness of 1.55 mm , and a mass of 2.50 g. What is its density?

Question

A round coin has a diameter of  19.55 mm , a thickness of  1.55 mm , and a mass of  2.50 g. What is its density?

Quizplus · Accepted Answer

To find the density, use the formula $\rho = \frac{m}{V}$, where $m$ is mass and $V$ is volume. The volume of the coin is calculated using the formula for the volume of a cylinder, $V = \pi r^2 h$, where $r$ is the radius ($\frac{19.55}{2} \, \text{mm}$) and $h$ is the thickness (1.55 mm). Convert dimensions to meters: $r = 0.009775 \, \text{m}$, $h = 0.00155 \, \text{m}$, and mass to kilograms ($2.50 \, \text{g} = 0.00250 \, \text{kg}$). Calculating the volume yields $V \approx 4.661 \times 10^{-7} \, \text{m}^3$. Thus, the density $\rho \approx \frac{0.00250}{4.661 \times 10^{-7}} \approx 5.37 \times 10^3 \, \text{kg/m}^3$.

A Round Coin Has a Diameter of 19 5.37×103 kg/m35.37 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }5.37×103 kg/m3

A Round Coin Has a Diameter of 19 $5.37 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$