Question

A metal cylinder has a mass of 6.20 g. The density of the cylinder is 21.0 g/mL. What is the volume​

Answer 1

`\boxed {\boxed {\sf v \approx0.295 \ mL}}`

Step-by-step explanation:

We are asked to find the volume of a metal cylinder. We are given the mass and the density.

We know that density is the mass per unit volume of a substance. It is found using the following formula.

`\rho= \frac {m}{v}`

We know the density is 21.0 grams per milliliter and the mass is 6.20 grams. We substitute these values into the formula.

• ρ= 21.0 g/mL
• m= 6.20 g

`21.0 \ g/mL = (6.20 \ g)/(v)`

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 the first denominator and the second numerator.

`\frac {21.0 \ g/mL}{1} = (6.20 \ g)/(v)`

`21.0 \ g/ mL *v= 6.20 \ g * 1`

`21.0 \ g/ mL *v= 6.20 \ g`

v is being multiplied by 21.0 grams per milliliter. The inverse operation of multiplication is division. Divide both sides of the equation by 21.0 g/mL.

`\frac {21.0 \ g/ mL *v}{21.0 \ g/mL}= (6.20 \ g )/(21.0 \ g/mL)`

`v= (6.20 \ g )/(21.0 \ g/mL)`

The units of grams cancel.

`v= (6.20 )/(21.0 mL)`

`v=0.2952380952`

The original measurements of density and mass both have 3 significant figures, so our answer must have the same. For this number, 3 sig fig is the thousandth place. The 2 in the ten-thousandth place tells us to leave the 5.

`v \approx0.295 \ mL`

The volume of the metal cylinder is approximately 0.295 milliliters.