Answer:
[tex]\boxed {\boxed {\sf v \approx 0.22 \ cm^3}}[/tex]
Explanation:
We are asked to find the volume of a substance.
We are given the density and the mass. The density of a substance is its mass per unit volume. The formula for calculating density is:
[tex]\rho= \frac{m}{v}[/tex]
We know the density of the substance is 13.6 grams per cubic centimeter and the mass is 3.0 grams.
Substitute these values into the formula.
[tex]13.6 \ g/cm^3= \frac{3.0 \ g }{v}[/tex]
We are solving for the volume, so we must isolate the variable v. First, cross multiply. Multiply the first numerator by the second denominator, then multiply the first denominator by the second numerator.
[tex]\frac{13.6 \ g/cm^3}{1}= \frac{3.0 \ g }{v}[/tex]
[tex]13.6 \ g/cm^3 *v =3.0 \ g *1[/tex]
Multiply on the right side of the equation.
[tex]13.6 \ g/cm^3 *v =3.0 \ g[/tex]
The variable is being multiplied by 13.6 grams per cubic centimeters. The inverse operation of multiplication is division, so we divide both sides of the equation by 13.6 g/cm².
[tex]\frac {13.6 \ g/cm^3 *v}{13.6 \ g/cm^3} =\frac{3.0 \ g }{13.6 \ g/cm^3}[/tex]
[tex]v =\frac{3.0 \ g }{13.6 \ g/cm^3}[/tex]
The units of grams cancel.
[tex]v =\frac{3.0 }{13.6 \ cm^3}[/tex]
[tex]v= 0.2205882353 \ cm^3[/tex]
The original measurement of density has 3 significant figures and the measurement of mass has 2. Our answer must have the least number of sig figs, which is 2. For the number we found, that is the hundredth place. The 0 in the thousandth place tells us to leave the 2 in the hundredth place.
[tex]v \approx 0.22 \ cm^3[/tex]
The volume of the substance is approximately 0.22 cubic centimeters.
