Density Sample Problems

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Sample Problems:   Solving for density
Solving for volume
Solving for mass
Problem number one (solving for density):

A piece of wood has a mass of 35 grams.  If its volume is 7 cm3, What is its density?

In order to solve this we have to do some different steps.  First we write the formula as we intend to use it.  Second, we place the numbers into the formula where they go (called the set-up) and lastly we do the mathematical calculations to attain the answer.

Step One: Write the formula as we need to use it.  In this question, they are asking for Density. So we are going to write the formula solving for that. Formula:  D = m / v
Step Two: Now we have to figure out what value goes for each letter:  the M and the V.  In this problem, it tells us the mass is 35g  and the volume is 7 cm3.  So put them in the formula. D = 35g / 7cm3
Step Three: Now the last and easiest part, do the math.  Be sure you keep your units with your problem.  For example, in this one, its units will be g/cm3 since that is what we did mathematically. 5 g/cm3
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Problem number two (solving for volume):

The density of a substance is 7.8 g/cm3.  What volume does 39 grams of it take up?

In order to solve this we have to do some different steps.  First we write the formula as we intend to use it.  Second, we place the numbers into the formula where they go (called the set-up) and lastly we do the mathematical calculations to attain the answer.

Step One: Write the formula as we need to use it.  In this question, they are asking for Volume. So, using the triangle, we are going to write the formula solving for that.  Cover up the V and write the function the other two variables will be doing. Formula:  v = m / D
Step Two: Now we have to figure out what value goes for each letter:  the D and the m.  In this problem, it tells us the mass is 39g  and the density is 7.8 g/cm3.  So put them in the formula. V = 39g / 7.8g/cm3
Step Three: Now the last and easiest part, do the math.  Be sure you keep your units with your problem.  For example, in this one, its units will be cm3 since when we divide the g by g/cm3, the grams cancel and leave just the cm3 5 cm3
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Problem number three (solving for mass):

The density of water is 1 g/ml.  What mass does 30 ml of water have?

In order to solve this we have to do some different steps.  First we write the formula as we intend to use it.  Second, we place the numbers into the formula where they go (called the set-up) and lastly we do the mathematical calculations to attain the answer.

Step One: Write the formula as we need to use it.  In this question, they are asking for Mass So, using the triangle, we are going to write the formula solving for that.  Cover up the m and write the function the other two variables will be doing. Formula:  m = D x v
Step Two: Now we have to figure out what value goes for each letter:  the D and the v.  In this problem, it tells us the volume is 30ml  and the density is 1 g/ml  So put them in the formula. m = 1 g/ml x 30 ml
Step Three: Now the last and easiest part, do the math.  Be sure you keep your units with your problem.  For example, in this one, its units will be g since when we multiple the g/ml by g, the ml cancel and leave just the g 30 g
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