The density of gold is $19.3 g / cm ^3$. What is the volume of a 13 g gold nugget? (Density: $D=\frac{m}{v}$ )
Answer (1)
We are given the density and mass of a gold nugget and asked to find its volume.
We rearrange the density formula to solve for volume: v = D m .
We substitute the given values: v = 19.3 13 .
We calculate the volume: v ≈ 0.6736 c m 3 , so the final answer is 0.6736 c m 3 .
Explanation
Understanding the Problem We are given the density of gold as 19.3 g / c m 3 and the mass of a gold nugget as 13 g. We need to find the volume of the gold nugget using the formula for density: D = v m , where D is density, m is mass, and v is volume.
Rearranging the Formula To find the volume, we rearrange the density formula to solve for v : v = D m .
Substituting the Values Now, we substitute the given values into the formula: m = 13 g and D = 19.3 g / c m 3 . Therefore, v = 19.3 13 c m 3 .
Calculating the Volume Calculating the volume: v = 19.3 13 ≈ 0.6736 c m 3 .
Final Answer The volume of the 13 g gold nugget is approximately 0.6736 c m 3 .
Examples
Imagine you have a small gold nugget and want to determine its volume without using water displacement. Knowing the density of gold allows you to calculate the volume simply by weighing the nugget. This principle is useful in various fields, such as geology for estimating mineral quantities or in jewelry making for determining the amount of gold needed for a piece.
