Difference between revisions of "Calculate Volume and Density"

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Volume is the amount of space an object occupies while density is the mass of an object per unit volume.<ref>http://uncw.edu/chem/Courses/Reeves/OnLineLabs/scienceMajors/Density_PH.pdf</ref> You need to know the volume of an object before you can calculate its density. Calculating volume for regular objects can be done with a simple formula determined by the shape of the object. Common units for volume are cubic centimeters (cm<sup>3</sup>), cubic meters (m<sup>3</sup>), cubic inches (in<sup>3</sup>), and cubic feet (ft<sup>3</sup>). Once you have the volume, density is one more simple calculation away. Common units for density are grams per cubic centimeter (g/cm<sup>3</sup>) or grams per milliliter (g/mL).  
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Volume is the amount of space an object occupies while density is the mass of an object per unit volume.<ref name="rf1">http://uncw.edu/chem/Courses/Reeves/OnLineLabs/scienceMajors/Density_PH.pdf</ref> You need to know the volume of an object before you can calculate its density. Calculating volume for regular objects can be done with a simple formula determined by the shape of the object. Common units for volume are cubic centimeters (cm<sup>3</sup>), cubic meters (m<sup>3</sup>), cubic inches (in<sup>3</sup>), and cubic feet (ft<sup>3</sup>). Once you have the volume, density is one more simple calculation away. Common units for density are grams per cubic centimeter (g/cm<sup>3</sup>) or grams per milliliter (g/mL).  
  
[[Category:Physics]]
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[[Category: Physics]]
  
 
== Steps ==
 
== Steps ==
 
=== Calculating the Volume of Regular Object ===
 
=== Calculating the Volume of Regular Object ===
 
#Determine the shape of your object. Knowing the shape of an object allows you to choose the proper formula and make the necessary measurements to calculate the volume.
 
#Determine the shape of your object. Knowing the shape of an object allows you to choose the proper formula and make the necessary measurements to calculate the volume.
#* A '''sphere''' is a perfectly round three-dimensional object, in which every point on the surface is an equal distance from the center. In other words, a sphere is a ball-shaped object.<ref>https://www.mathsisfun.com/definitions/sphere.html</ref>
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#* A '''sphere''' is a perfectly round three-dimensional object, in which every point on the surface is an equal distance from the center. In other words, a sphere is a ball-shaped object.<ref name="rf2">https://www.mathsisfun.com/definitions/sphere.html</ref>
#* A '''cone''' is a 3-dimensional solid that has a circular base and a single vertex (the point of the cone). Another way to think of this is that a cone is a special pyramid that has a circular base.<ref>http://www.mathopenref.com/cone.html</ref>
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#* A '''cone''' is a 3-dimensional solid that has a circular base and a single vertex (the point of the cone). Another way to think of this is that a cone is a special pyramid that has a circular base.<ref name="rf3">http://www.mathopenref.com/cone.html</ref>
#* A '''cube''' is a three-dimensional shape that has six identical square faces.<ref>https://www.mathsisfun.com/definitions/cube.html</ref>
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#* A '''cube''' is a three-dimensional shape that has six identical square faces.<ref name="rf4">https://www.mathsisfun.com/definitions/cube.html</ref>
#* A '''rectangular solid''', also known as a rectangular prism, is similar to a cube in that it is a three-dimensional shape with six sides, but in this case, the sides are rectangular instead of square.<ref>http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_3Dprisms.xml</ref>
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#* A '''rectangular solid''', also known as a rectangular prism, is similar to a cube in that it is a three-dimensional shape with six sides, but in this case, the sides are rectangular instead of square.<ref name="rf5">http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_3Dprisms.xml</ref>
#* A '''cylinder''' is a three-dimensional shape that has two identical flat ends that are circular in shape, and a single curved side that connects them.<ref>https://www.mathsisfun.com/definitions/cylinder.html</ref>
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#* A '''cylinder''' is a three-dimensional shape that has two identical flat ends that are circular in shape, and a single curved side that connects them.<ref name="rf6">https://www.mathsisfun.com/definitions/cylinder.html</ref>
#* A '''pyramid''' is a three-dimensional shape with a polygon for a base, and lateral faces that taper at an apex (the point of the pyramid).<ref>http://www.mathwords.com/p/pyramid.htm</ref> A regular pyramid is a pyramid in which the base of the pyramid is a regular polygon, meaning that all of the sides of the polygon are equal in length, and all of the angles are equal in measure.<ref>http://www.mathwords.com/r/regular_pyramid.htm</ref>
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#* A '''pyramid''' is a three-dimensional shape with a polygon for a base, and lateral faces that taper at an apex (the point of the pyramid).<ref name="rf7">http://www.mathwords.com/p/pyramid.htm</ref> A regular pyramid is a pyramid in which the base of the pyramid is a regular polygon, meaning that all of the sides of the polygon are equal in length, and all of the angles are equal in measure.<ref name="rf8">http://www.mathwords.com/r/regular_pyramid.htm</ref>
 
#* If your object has an irregular shape, you can use the displacement method to determine volume.
 
#* If your object has an irregular shape, you can use the displacement method to determine volume.
 
#Choose the correct equation to calculate volume. Each shape has its own formula that calculates how much three-dimensional space that object occupies. Below are the formulas for the objects listed above. Check out [[Calculate Volume|How to Calculate Volume]] for more detailed notes and images on these formulas.  
 
#Choose the correct equation to calculate volume. Each shape has its own formula that calculates how much three-dimensional space that object occupies. Below are the formulas for the objects listed above. Check out [[Calculate Volume|How to Calculate Volume]] for more detailed notes and images on these formulas.  
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=== Calculating the Volume of an Irregular Object ===
 
=== Calculating the Volume of an Irregular Object ===
#Calculate the volume of the object using displacement. Measuring dimensions of objects that are irregularly shaped can be difficult and lead to inaccurate measurements and calculations of volume. By measuring the amount of water displaced by an object, you can easily determine its volume without complex formulas.<ref>http://teachertech.rice.edu/Participants/bradshaw/lessons/elements/density.html</ref>
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#Calculate the volume of the object using displacement. Measuring dimensions of objects that are irregularly shaped can be difficult and lead to inaccurate measurements and calculations of volume. By measuring the amount of water displaced by an object, you can easily determine its volume without complex formulas.<ref name="rf9">http://teachertech.rice.edu/Participants/bradshaw/lessons/elements/density.html</ref>
 
#* This method can also be used to determine the volume of a regular shape.
 
#* This method can also be used to determine the volume of a regular shape.
 
#Fill a graduated cylinder with water. A graduated cylinder is a piece of lab equipment that has graduated markings on the outside and allows you to measure the volume of liquids. Make sure the graduated cylinder is large enough to contain your object. You want to fill it with enough water to completely submerge the object, but not overflow. Record the starting water level of the beaker.
 
#Fill a graduated cylinder with water. A graduated cylinder is a piece of lab equipment that has graduated markings on the outside and allows you to measure the volume of liquids. Make sure the graduated cylinder is large enough to contain your object. You want to fill it with enough water to completely submerge the object, but not overflow. Record the starting water level of the beaker.
#* When you record the starting volume of water, be sure to look at the water at eye level and record the value at the bottom of the meniscus. The meniscus is the curve that the water takes when it comes in contact with another surface.<ref>http://water.usgs.gov/edu/meniscus.html</ref>
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#* When you record the starting volume of water, be sure to look at the water at eye level and record the value at the bottom of the meniscus. The meniscus is the curve that the water takes when it comes in contact with another surface.<ref name="rf10">http://water.usgs.gov/edu/meniscus.html</ref>
 
#Gently place the object in the beaker. Take care not to drop the object in the water as this can lead to some water splashing out of the graduated cylinder. Ensure that your object is fully submerged. Record the new water level of the beaker, again at eye level paying close attention to the meniscus.
 
#Gently place the object in the beaker. Take care not to drop the object in the water as this can lead to some water splashing out of the graduated cylinder. Ensure that your object is fully submerged. Record the new water level of the beaker, again at eye level paying close attention to the meniscus.
 
#* If any water overflows when you place the object in the beaker, try again with a larger graduated cylinder or use less water.  
 
#* If any water overflows when you place the object in the beaker, try again with a larger graduated cylinder or use less water.  
#Subtract the new water level from the starting water level. The amount of water the object displaces is equal to the volume of the object itself measured in cubic centimeters. Liquids are generally measured in milliliters, however, one milliliter is equal to one cubic centimeter.<ref>http://classroom.synonym.com/ways-determine-density-2508.html</ref>
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#Subtract the new water level from the starting water level. The amount of water the object displaces is equal to the volume of the object itself measured in cubic centimeters. Liquids are generally measured in milliliters, however, one milliliter is equal to one cubic centimeter.<ref name="rf11">http://classroom.synonym.com/ways-determine-density-2508.html</ref>
 
#* For example, if you started with 35 mL of water and ended with 65 mL of water, the volume of your object is 65 – 35 = 30 mL or 30 cm<sup>3</sup>
 
#* For example, if you started with 35 mL of water and ended with 65 mL of water, the volume of your object is 65 – 35 = 30 mL or 30 cm<sup>3</sup>
  
 
=== Calculating Density ===
 
=== Calculating Density ===
#Determine the mass of the object. The amount of matter in an object is the mass of that object.<ref>http://teachertech.rice.edu/Participants/bradshaw/lessons/elements/density.html</ref> It is measured directly by weighing the object on a scale and its unit is grams.
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#Determine the mass of the object. The amount of matter in an object is the mass of that object.<ref name="rf9" /> It is measured directly by weighing the object on a scale and its unit is grams.
 
#* Find an accurate scale and place the object on it. Record its mass in your notebook.
 
#* Find an accurate scale and place the object on it. Record its mass in your notebook.
 
#* You can also measure mass with a balance. With your object on one side, place weights of known mass on the other side until both sides of the scale are balanced. The mass of your object is equal to the total mass of the balance weights.
 
#* You can also measure mass with a balance. With your object on one side, place weights of known mass on the other side until both sides of the scale are balanced. The mass of your object is equal to the total mass of the balance weights.
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&= \frac{24 {\rm \ g }}{8 {\rm \ cm^{3} }} \\
 
&= \frac{24 {\rm \ g }}{8 {\rm \ cm^{3} }} \\
 
&= 3 {\rm \ g \ cm^{-3} }\end{align}</math>  
 
&= 3 {\rm \ g \ cm^{-3} }\end{align}</math>  
== Video ==
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{{Video:Calculate Volume and Density|}}
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== Tips ==
 
== Tips ==