Density and Specific Gravity - Practice Problems
Jump to: Rock and Mineral density | Rock and mineral specific gravity You can download the questions (Acrobat (PDF) 25kB Jul24 09) if you would like to work them on a separate sheet of paper.
Calculating densities of rocks and minerals
`Volume\times Density=Mass` You can then divide both sides by density to get volume alone: `Volume=\frac{Mass}{Density}` By substituting in the values listed above, `Volume=\frac{2000\ kg}{3200\ \frac{kg}{m^{3}}}`
So the volume will be 0.625 m 3 Note that the above problem shows that densities can be in units other than grams and cubic centimeters. To avoid the potential problems of different units, many geologists use specific gravity (SG), explored in problems 8 and 9, below.
`text{volume}=text{length}\times text{width}\times text{height}` .
The volume of the cube is
`2cm\times2cm\times2cm=8cm^{3}` . The density then is the mass divided by the volume: `Density=\frac{Mass}{Volume}` `Density=\frac{40g}{8cm^{3}}=5.0\frac{g}{cm^{3}}` Thus the cube is NOT gold , since the density (5.0 g/cm 3 ) is not the same as gold (19.3 g/cm 3 ). You tell the seller to take a hike . You might even notice that the density of pyrite (a.k.a. fool's gold) is 5.0 g/cm 3 . Luckily you are no fool and know about density!
Calculating Specific Gravity of Rocks and Minerals
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Density Calculations – Worked Example Problem
Density is the measurement of the amount of mass per unit volume. Density calculations are done using the formula:
Example Problems: 1. Calculate the density in g/mL of 30 mL of solution that weighs 120 grams. 2. Calculate the density in g/mL of 0.4 L of solution weighing 150 grams. 3. Calculate the density in g/mL of 3000 mL of solution weighing 6 kg.
Example 2 We want to know the density in g/mL, but our volume is in liters. First, convert the volume to mL.
Example 3 Again, we want g/mL, and our mass is in kg. Convert the mass to grams.
Related Posts
Density – problems and solutions
Wanted : density (ρ)
Density (ρ) = 250 g/cm 3
m = ρ V = (250 g/cm 3 )(5 cm 3 ) = 1250 gram
3. Volume of water is 35 cm 3 and mass of water is 60 gram, what is the density of the water.
4. Mass of an metal is 120 gram and volume of an metal is 60 cm 3 . What is the density of the metal?
ρ = density, m = mass, V = volume
Wanted : density
Volume (V) = volume of spilled water = 40 ml
0.04 liters = (0.04)(0.001) m 3 = 0.00004 m 3
Mass (m) = 100 gram + 20 gram = 120 gram = 120 / 1000 kilogram = 0.120 kilogram
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M D = –––– V 25.1 g 13.6 g/cm 3 = –––––– V V = 1.845588 cm 3
M D = –––– V M 11.4 g/cm 3 = –––––––––––– 1.845588 cm 3 V = 21.0 g
V Pb = V Hg
M Pb V Pb = –––– D Pb and M Hg V Hg = –––– D Hg
M Pb M Hg –––– = –––– D Pb D Hg
M Pb 25.1 –––– = –––– 11.4 13.6 M Pb = 21.0 g
Density = mass / volume rearrange to: Volume = mass / density V = 2.25 g / 2.70 g/cm 3 = 0.83 cm 3 Note: since 1 mL = 1 cm 3 , this is 0.83 mL
11.20 mL + 0.83 mL = 12.03 mL
(a) Calculate the volume (density of Al = 2.70 g cm¯ 3 (b) Calculate the thickness of the piece of Al in mm
1.50 g / 2.70 g/cm 3 = 0.555555 cm 3 (answer to a) 0.555555 cm 3 = (x) (24.0 cm) (30.0 cm) x = 0.000772 cm (to 3 sig figs) There are 10 mm in one cm, so divide the cm answer by 10 to get the thickness in mm. 0.0000772 mm (answer to b)
That means 92.276 cm 3 is Zn and 7.724 cm 3 is Cu.
(92.276 cm 3 ) (7.14 g/cm 3 ) = 658.85064 g (7.724 cm 3 ) (8.96 g/cm 3 ) = 69.20704 g
728.05768 g / 100. cm 3 = 7.28 g/cm 3 (that's the answer to three sig figs)
1.00 x 10 5 kg = 1.00 x 10 8 g 1.00 x 10 8 g / 6.62 g cm¯ 3 = 1.51 x 10 7 cm 3 1.51 x 10 7 cm 3 3 = 247 cm = 2.47 m
D = m / V V = m / D V = 71.7 g / 7.87 g/cm 3 V = 9.11 cm 3
63.0 mL + 9.11 mL = 72.1 mL (rounded off to the proper number of sig figs)
V = 71.7 g Fe x (1 cm 3 / 7.87 g Fe) = 9.11 cm 3
Let us assume 1.00 cm 3 of Al is present. That means 2.70 g of Al is present. In the rod of tin that is hollow, the mass of tin present weighs 2.70 g. We know this because the average densities of the two rods are equal. Remember, the average density of the tin rod includes the empty space. What volume of solid tin is required to provide 2.70 g? The answer is 0.370 cm 3 (from 2.70 g divided by 7.31 g/cm 3 ). The rest of the tin rod must be hollow. This is 0.670 cm 3 . Since the overall volume was 1.00 cm 3 , the fraction of the tin rod that is hollow is 0.670
Identical external dimensions means overall volume is the same for both rods. Let's call that V. It must be that mass Al = mass Sn. So, let's convert from volume Al to volume Sn with equivalent mass: 2.70 g Al 1 g Sn 1 cm 3 V x ––––––– x ––––––– x ––––––– = 0.370V 1 cm 3 1 g Al 7.31 g Sn
(V − 0.370V) / V 1 − 0.370 = 0.630
Kilograms will be changed to grams by multiplying the numerator by 1000. Liters will be changed to mL by multiplying the denominator by 1000. Those two multiplications cancel each other out. And one mL equals one cm 3 . The answer is 22.59 g/cm 3 . Here's a dimensional analysis set up showing the solution: 22.59 kg 1000 g 1 L 1 mL ––––––– x –––––– x ––––––– x ––––– = 22.59 g/cm 3 1 L 1 kg 1000 mL 1 cm 3
One mole of gold weighs 196.9665 g. V = mass / density = 196.9665 g / 19.32 g cm¯ 3 = 10.195 cm 3 The formula for volume of a cylinder is V = πr 2 L The length (L) of the wire is therefore: L = 10.195 cm 3 / [(3.14159) (0.05000 cm) 2 ] = 1298 cm By the way, note the 0.05 cm for the radius. The wire was 1 mm in diameter, which is 0.1 cm. And then half of that for the radius is 0.05 cm.
0.050 L = 50. mL = 50. cm 3 (11.34 g/cm 3 ) (50. cm 3 ) = 567 g 0.50 kg = 500 g The 0.050 L contains more mass.
0.50 kg = 500 g 500 g / 11.34 g/cm 3 = 44.1 cm 3 44.1 cm 3 = 44.1 mL = 0.0441 L The larger volume has the greater mass since both samples are lead. The answer to the problem is 0.050 L.
0.500 lb / 0.4098 lb/in 3 = 1.22 in 3
1 inch = 2.54 cm (1.00 in) 3 = (2.54 cm) 3 1.00 in 3 = 16.387 cm 3
11.34 g 16.387 cm 3 –––––– x –––––––– = 185.828 g/in 3 cm 3 in 3
0.500 lb = 226.796 g
1 in 3 226.796 g x –––––––– = 1.22 in 3 185.828 g
Density, Area and Volume
Related Topics: Common Core (Geometry) Common Core for Mathematics
Examples, solutions, videos, and lessons to help High School students learn how to apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
Common Core: HSG-MG.A.2
Density, Mass and Volume How to use the Density Mass Volume formula triangle and find volume of shapes. It goes through a couple of examples of finding mass. Example:
- The density of this metal block is 5 g/cm 3 . Find the mass of the block.
- The density of this prism is 4 g/cm 3 . Find the mass of the prism.
Density Word Problems Simple problems dealing with density formula (D = m / v). Example:
- What is the density of an aluminum metal block that has a mass of 27.0 g and a volume of 10.0 cm 3 ?
- What is the density of a steel block that has a mass of 7.8 g and a volume of 1.0 cm 3 ?
- What is the density of a nail that has a mass of 12.5 g and a volume of 1.6 cm 3 ?
- On Great Skies Airlines a carry-on suitcase can be no more than 12 kg and 30,000 cm 3 . Does the following suitcase qualify as a carry-on.
Density Calculations Solving density word problems using the formula triangle. Example:
- A loaf of bread has a volume of 2,270 cm 3 and a mass of 454 g. Whas the density of the bread?
- What is the volume of a tank that can hold 18.754 g of methanol whose density is 0.788 g/cm 3 ?
- A bottle has a capacity of 1.2 liters. If the density of ether is 0.74 g/ml., what mass of ether can the bottle hold?
Density Facts and Practice Problems Learn more about density and practice calculating using word problems. Density is how much mass is contained in a given volume? Example:
- What is the density of carbon dioxide gas if 0.196 g occupies a volume of 100 mL?
- A block of wood 3 cm on each side has a mass of 27 g. What is the density of the block?
- A 10.0 cm 3 sample of copper has a mass of 89.6 g. What is the density of copper?
Density Practice Problems This video shows the equation for Density and gives 2 example problems. Example:
- What is the density of a bolt that has a mass of 14 g and a volume of 2 ml?
- What is the volume of a liquid silver sample that has a density of 0.125 g/ml and a mass of 1.2g?
What is BTU (British Thermal Unit)? A short explanation of how to calculate water temperature rise in ц, given certain BTUs per hour.
Understanding the BTU - Energy produced
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Density Worked Example Problem
Calculating Density of a Substance
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Density is a measure of how much matter is in a space. It is expressed in units of mass per volume, such as g/cm 3 or kg/L. This is a worked example of how to calculate the density when given the volume and mass of a substance.
Sample Density Problem
A brick of salt measuring 10.0 cm x 10.0 cm x 2.0 cm weighs 433 grams. What is its density? Solution: Density is the amount of mass per unit volume, or: D = M/V Density = Mass/Volume Step 1: Calculate Volume In this example, you are given the dimensions of the object, so you have to calculate the volume. The formula for volume depends on the shape of the object, but it's a simple calculation for a box:
Volume = length x width x thickness Volume = 10.0 cm x 10.0 cm x 2.0 cm Volume = 200.0 cm 3 Step 2: Determine Density
Now you have the mass and the volume, which is all the information you need to calculate density. Density = Mass/Volume Density = 433 g/200.0 cm 3 Density = 2.165 g/cm 3 Answer: The density of the salt brick is 2.165 g/cm 3 .
A Note About Significant Figures
In this example, the length and mass measurements all had 3 significant figures . So, the answer for density should also be reported using this number of significant figures. You'll have to decide whether to truncate the value to read 2.16 or whether to round it up to 2.17.
- How to Calculate Density - Worked Example Problem
- Density Example Problem: Calculate Mass From Density
- How to Calculate Density of a Gas
- Heat of Formation Worked Problem
- Calculate Simplest Formula From Percent Composition
- Molality and Concentration of a Chemical Solution
- Theoretical Yield Worked Problem
- Percent Composition by Mass Example
- How to Find Mass of a Liquid From Density
- Heat Capacity Example Problem
- Convert Frequency to Wavelength Worked Example Problem
- Freezing Point Depression Example Problem
- How to Calculate Experimental Error in Chemistry
- How to Calculate Mass Percent Composition
- Acids and Bases: Calculating pH of a Strong Acid
- Mole Relations in Balanced Equations
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Chem – Density Problem Solving
What sections should I know before attempting to learn this section?
—> Introduction to Units
—> Unit Prefixes
—> Introduction to Problem Solving
How do you solve density word problems?
To help further your problem solving skills, I will introduce you to the concept of density. Density is the mass per unit volume. Another way to state that is the mass divided by the volume. See equation below:
| Density = | mass |
| volume | |
| 1 | |
| D = | m |
| V |
The letter D represents Density , the letter m represents mass , and the letter V represents volume . The density equation has 3 variables. That means in a problem where you have to use density, you will be given 2 variables and asked to solve for the 3 rd . Density can have different units like (g/mL) or (g/L) or (kg/L) or (mg/mL) just to name a few. How do we use it to solve some equations? Look to the demonstrated examples below.
VIDEO Density Problem Solving Demonstrated Example 1 : What is the density for a mass that is 345g and 789mL?
Step 1: highlight number and units
What is the density for a mass that is 345g and 789mL ?
Step 2 : write numbers and units
mass = 345g
volume = 789mL
Step 3 : restate the question
density = ?
Now what is a formula or concept that relates together mass, volume, and density?
Answer: the density formula (so write down the density formula below)
| D = | m |
| V |
Answer: fill in the numbers and units from your steps 1 through 3.
| D = | 345g |
| 789mL |
Solve for density (D)
Answer: 245g / 789mL = 0.437g/mL
COMPLETE ANSWER: D = 0.437g/mL
VIDEO Density Problem Solving Demonstrated Example 2 : What is the volume of an object that is 154g and has a density of 67g/L?
Step 1: highlight numbers and units
What is the volume of an object that is 154g and has a density of 67g/L ?
mass = 154g
density = 67g/L
Step 3 : restate question
| 67g/L = | 154g |
| V |
How do you solve for volume?
Answer: First multiply both sides by V
| V * 67g/L = | 154g * V |
| V |
Cross out V on the right side
| V * 67g/L = | 154g * V |
| V |
| V * 67g/L = | 154g |
| 1 |
Now divide both sides by 67g/L (red)
| V * 67g/L = | 154g |
| 67g/L | 67g/L |
Cross out 67g/L on the left side
| V * 67g/L = | 154g |
| 67g/L | 67g/L |
| V = | 154g |
| 67g/L |
Solve for V
Answer: 154 / 67 = 2.30 L
COMPLETE ANSWER: V = 2.30 L
PRACTICE PROBLEMS : Solve for the missing variable in the word problem.
What is the density of an object with a mass of 25g and a volume of 47mL?
Answer: 0.53g/ml
What is density of something that is 36L and 97g?
Answer: 2.69g/L
What is the mass of a cube that has a density of 42g/mL and a volume of 520mL?
Answer: 21840g
An object is 34L and 369g/L. What is the mass of the object?
Answer: 12546g
What is the volume of an object that has a density of 74g/mL and a mass of 58g?
Answer: 0.78ml
If an object is 23kg and 4kg/L. What is the volume?
Answer: 5.75L
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Density Mass Volume Calculator
Table of contents
With this density mass volume calculator, you are free to enter any two of these values, and the calculator will instantly calculate the third value. This short article covers:
- How to calculate volume with density and mass and other combinations.
- How to use this density mass volume calculator.
- What is the density of a cork, and how to calculate it.
Density mass and volume equations
The density of an object is defined as the mass per unit volume and is mathematically expressed as:
- ρ \rho ρ – Density of the substance;
- m m m – Mass (or weight, if measured on Earth); and
- V V V – Volume.
We can then rearrange this equation to express the mass in terms of density and volume:
Finally, by rearranging the equation one final time, we can calculate the volume of an object if the mass and density are known:
This density mass volume calculator contains all three of these equations, making it very flexible to your needs.
How to use this density mass volume calculator
It couldn't be easier to use this calculator. All you have to do is enter any two values to calculate the third value. Let's go through an example just to make sure it's clear in your mind.
- You know the density of the object is 10490 kg/m 3 , so enter this value in the density field of the calculator. Make sure you select the appropriate unit for each variable before entering the value.
- The mass of the object is 6 kg , so go ahead and enter this value into the second row of the calculator.
- Oh, look! You've got your answer. Change the volume units to cm 3 , and the value for the volume is 572 cm 3 .
Other density-related calculators
Omni has a wide range of density calculators, if you would like to explore this topic further:
- Density calculator ;
- Gas density calculator ;
- Mass to density calculator ;
- Volume to density calculator ;
- Density to mass calculator ;
- Density to weight calculator ;
- Cube density calculator ;
- Density of a cylinder calculator ; and
- Sphere density calculator .
How do I calculate volume with density and mass?
To calculate the volume of an object if you know its density and mass:
- Weigh the mass of the object.
- Lookup the density of the material the object is made from.
- Divide the mass by the density.
- Enjoy your result for the volume of the object.
Mathematically, volume is given by the equation: volume = mass / density .
What is the density of a cork?
240 kg/m 3 or 14.98 lb/ft 3 . The volume of a champagne cork is around 37.5 cm 3 and its weight is 9 grams. To calculate the density, divide the weight by the volume: 9 g / 37.5 cm 3 = 0.24 g/cm 3 = 240 kg/m 3 .
Same as weight, if the object is weighed on Earth.
Tip: Use the "Calculate volume" section below to calculator the volume by entering the length, width & height.
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ol{padding-top:0;}.css-63uqft ul:not(:first-child),.css-63uqft ol:not(:first-child){padding-top:4px;} Calculate volume
Calculate the volume using dimensions
Length of a cuboid (box-shaped) object.
Width of a cuboid (box-shaped) object.
Height of a cuboid (box-shaped) object.
Density Calculations Quiz
This online quiz is intended to give you extra practice in calculating density, mass or volume of over 150 different materials in g/cm 3 , g/mL or kg/m 3 .
Select your preferences below and click 'Start' to give it a try!
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Density Calculator
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The density of a material, typically denoted using the Greek symbol ρ, is defined as its mass per unit volume.
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In this problem you need a volume, so you will need to rearrange the density equation to get volume. ... `Volume\times Density=Mass` You can then divide both sides by density to get volume alone: `Volume=\frac{Mass}{Density}` By substituting in the values listed above, `Volume=\frac{2000\ kg}{3200\ \frac{kg}{m^{3}}}` So the volume will be 0.625 m 3
Density Problems. On this page I put together a collection of density problems to help you better understand calculations involving density. Problem # 1. A solid ball has a mass of 50 grams and a volume of 20 cm 3. What is the density? (Answer: 2.5 g/cm 3) Problem # 2. A solid ball has a mass of 100 grams and a radius of 2 cm.
Step 2: Plug your variables into the density formula. density = mass/volume. density = 11.2 grams/8 cm 3. density = 1.4 grams/cm 3. Answer 1: The sugar cube has a density of 1.4 grams/cm 3. Question 2: A solution of water and salt contains 25 grams of salt in 250 mL of water.
m = mass. V = volume. Example Problems: 1. Calculate the density in g/mL of 30 mL of solution that weighs 120 grams. 2. Calculate the density in g/mL of 0.4 L of solution weighing 150 grams. 3. Calculate the density in g/mL of 3000 mL of solution weighing 6 kg.
This chemistry video tutorial explains how to solve density problems. It provides all of the formulas and equations you need such as finding the volume of a...
ρ = m / V = 0.120 kg / 0.00002 m 3 = 120 kg / 0.02 m 3 = 6000 kg/m 3. What is density? Answer: Density is a measure of how much mass is contained in a given volume.It is calculated by dividing the mass of an object by its volume: Density=MassVolume Density = Volume Mass . How does the density of an object relate to its ability to float or sink in a fluid?
Short Solution: 1) Look up the density of lead in pounds per cubic inch to find a value of 0.4098 lb/in 3 . 2) Divide 0.500 lb by density: 0.500 lb / 0.4098 lb/in 3 = 1.22 in 3. Long Solution, deliberately starting with metric density: 1) Look up the density of lead to find a value of 11.34 g/cm 3 .
Density, Mass and Volume, density formula triangle, Density Facts and Practice Problems, examples and step by step solutions, Common Core High School, Geometry, HSG-MG.A.2, BTU ... Solving density word problems using the formula triangle. Example: A loaf of bread has a volume of 2,270 cm 3 and a mass of 454 g. Whas the density of the bread?
Density = Mass/Volume. Step 1: Calculate Volume. In this example, you are given the dimensions of the object, so you have to calculate the volume. The formula for volume depends on the shape of the object, but it's a simple calculation for a box: Volume = length x width x thickness. Volume = 10.0 cm x 10.0 cm x 2.0 cm.
The letter D represents Density, the letter m represents mass, and the letter V represents volume.The density equation has 3 variables. That means in a problem where you have to use density, you will be given 2 variables and asked to solve for the 3 rd.Density can have different units like (g/mL) or (g/L) or (kg/L) or (mg/mL) just to name a few.
Not all density problems want you to actually calculate density. The formula involves density, mass, and volume. ... Whether you are solving for mass, density, or volume, you must keep careful watch over the units. The common type of mistake in rearranging the density formula is not properly checking the units at the end. If you are looking for ...
Learn how to use density as a conversion factor and how to find density. This video explains what the proper units are for density and how to get the correct...
To see all my Chemistry videos, check outhttp://socratic.org/chemistryWe'll practice solving density example problems. We'll look at how to use the density n...
A bottle of water has a density of 1000 kg/m ^3 and mass of 0.5 kg. Calculate the volume of the water bottle giving your answer in litres. [2 marks] We're looking for volume, so covering V, we must divide the mass by the density. So. \text { Volume } = \dfrac {0.5} {1000} = 0.0005 m ^3. Multiplying this by 1000 to convert into litres, gives ...
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The following two example problems demonstrate how to solve density problems using the density-mass-volume triangle. Example Problem 1: Solving Density Problems Gold has a density of {eq}19.3\ \rm ...
The Corbettmaths Practice Questions on Density. GCSE Revision Cards. 5-a-day Workbooks
Mathematically, volume is given by the equation: volume = mass / density. What is the density of a cork? 240 kg/m 3 or 14.98 lb/ft 3. The volume of a champagne cork is around 37.5 cm 3 and its weight is 9 grams. To calculate the density, divide the weight by the volume: 9 g / 37.5 cm 3 = 0.24 g/cm 3 = 240 kg/m 3.
This online quiz is intended to give you extra practice in calculating density, mass or volume of over 150 different materials in g/cm 3, g/mL or kg/m 3. Select your preferences below and click 'Start' to give it a try! Number of problems: 1. 5. 10. 25.
Density Calculator. Please provide any two values to the fields below to calculate the third value in the density equation of. The density of a material, typically denoted using the Greek symbol ρ, is defined as its mass per unit volume. The calculation of density is quite straightforward. However, it is important to pay special attention to ...
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