Answer:
[tex]\boxed {\boxed {\sf 4.67 \ g }}[/tex]
Explanation:
We are asked to calculate the mass of a sample of gold. We are given the density and volume.
Density is a substance's mass per unit volume. Therefore, the formula for calculating density is:
[tex]\rho= \frac{m}{v}[/tex]
The density is 19.3 grams per cubic centimeter and the volume is 0.242 cubic centimeters. Substitute the values into the formula.
[tex]19.3 \ g/cm^3 = \frac{m}{0.242 \ cm^3}[/tex]
We are solving for the mass of the gold sample, so the variable m must be isolated. It is being divided by 0.242 cubic centimeters. The inverse operation of division is multiplication. Multiply both sides of the equation by 0.242 cm³.
[tex]0.242 \ cm^3 * 19.3 \ g/cm^3 = \frac{m}{0.242 \ cm^3} * 0.242 \ cm^3[/tex]
[tex]0.242 \ cm^3 * 19.3 \ g/cm^3 = m[/tex]
The units of cubic centimeters cancel.
[tex]0.242 * 19.3 \ g = m[/tex]
[tex]4.6706 \ g = m[/tex]
The original measurements of mass and density both have 3 significant figures, so our answer must have the same. For this number, 3 sig fig is the hundredth place. The 0 in the thousandth place tells us to leave the 7.
[tex]4.67 \ g \approx m[/tex]
The mass of the gold sample is approximately 4.67 grams.
