How to find volume

There are several ways to calculate the volume of liquids and solids; even irregularly shaped objects.

To find the volume of a sharp edged block of wood follow this process.

1.  Here is the math equation:  Volume of the object is equal to its length
     multiplied by its width then multiplied by its height.  V=L X W X H

2.  Measure the object's length, width and height.  You will measure in
     centimeters up to one decimal accuracy.  Example:  10.4 cm

3.  You measure the length to be 10.4 cm, width 8.3, and height 4.2.

4.  Next you will multiple the length and width.   Then multiply that answer 
     by the height.
          a.  For scientific accuracy your answer cannot have anymore decimal
               places than decimal accuracy of the measurements.
          b.  Note the measurements are only measured to one decimal place...tenth
               of a centimeter.
          c.  This means to a scientist that answer can only be to the tenth of a cubic
               centimeter.
          d.  If the block had been measured to a hundredth of a centimeter, then the                answer would be to the hundredth of a cubic centimeter.
          e.  So calculate the volume of an object will always be cubic(some unit).
          f.  Now how do you place the decimal point in the answer below?
              i.     Just count the number of decimal places in the measurements.
              ii.   In the above measurements, there are three measurements with one
                    decimal place accuracy.
              iii.  So count the number spaces from the right to the left then place the
                    decimal point in your answer.

10.4 cm

X8.3 cm

312     

+832           

8632      

X 4.2      

17264       

+36528             

                                    362.544 cm3   (cubic centimeters)

Practice Problems

1.  Find the volume in cubic centimeters of this block of metal that has a length

     of 8.4 cm, a width of 6.6 cm, and a height of 4.2 cm.?

2.  What is the volume of a piece of wood that is 11.2 cm long, 8.5 cm wide, and

     4.7 cm thick (height measurement)?

3.  A square piece of wood has a length, width, and height of 8.21 cm.  What is 

     its volume?

Volume of a Liquid

1.  To find the volume of a liquid you would use a graduated cylinder and 

             pour the liquid in the cylinder.

2.  You look at the liquid in the cylinder to see how much liquid in milliliters.

3.  To find the correct volume look at the cylinder eye-level.
4.  You will notice there is a curved waterline.
     a.  One of my students once said it looks like a contact lens upside down on               the top of the liquid.
5.  At the bottom of the curved line is where you  look to find the correct volume      in milliliters.  This curved line is called the meniscus. 

(from quantum.esu.edu)

(from www.thetechieteacher.net)

         

Volume of an irregularly shaped object

1.   First pour water into the cylinder to a certain volume...30 mL.
2.  Then carefully lower the object into the cylinder so as not to splash out any           water.
3.   Place the cylinder on a flat surface.
4.  Look at the water level at eye level and record the new volume level in
     milliliters.

5.  To find the volume of the object you will subtract the being volume before the      object was put in the cylinder from the volume of the water after the object

     was placed in the cylinder.

Example:   If you pour water into the graduated cylinder to the 25 mL line. Then add in the small rock...of it has to be smaller than the cylinder... and see what is the new level in the cylinder.  Say the new level is 42 mL.  Subtract the 25 mL from the 42 mL and you now know the volume of the small rock.  It is? Good answer!!!

     Of course the larger the object the larger the graduated cylinder.  If you have a really large object like a human body, this is what you would do.

1.  For large objects, you will use a container large enough to hold the object.
2. The container is filled with water until the water is just ready to flow out the
    container's spout.

3. Then have a way to measure the amount of water that flows out when the 

    object is carefully placed in the large water filled container.  

4. The amount of the water that flows out will show the volume of the object in
     milliliters or liters.

Decimals mean accuracy of measurement in science.

       This is where the scientific accuracy is applied.  This is not like in math where you do not round your answer.  But because the measurements were only accurate to one decimal place, your answer can only be accurate to one decimal place.  So the science answer is 362.5 cm3.

     Unlike math...in science measurements the number of decimal places indicates the accuracy of the measurements.  So if you have an answer of 3.4; it is not as accurate as an answer of 3.421.  In science even a zero behind the decimal point means accuracy where 4.000 is a lot much accurate than 4.0 or even 4.  If you had an answer of 4, this means your measurements were made as whole numbers.  For scientific accuracy your answer cannot have anymore decimal places than the number decimal places used in the measurements.  4 whole number, 4.1 measured to a tenth, 4.12 measured to a hundredth, 4.123 measured to a thousandth, and 4.1234 measured to a ten thousandth.

          Note the measurements on the block of wood were only measured to one decimal place...tenth of a centimeter.  This means to a scientist that the answer can only be to the tenth of a cubic centimeter.  If the block had been measured to a hundredth of a centimeter, then the answer would be to the hundredth of a cubic centimeter.  Did you know that 1 cubic centimeter is equal to 1 milliliter?

     Science Math Note

          Here is something else that is different in science.  When you read the answer from your measurements or the answer after your calculations is different in math and science. In math it would read fifty-three and 8 tenths cubic centimeters.  In science we read it as fifty-three point 8 cubic centimeters.  My experience as a science teacher is: when in science read the answer as a science answer and when in math read answer as a math answer.

          Case in point.   Where science is better for communication of data.  If you had a number that looks like this:  34.793 cm.  Would it be easier to read it as thirty-four and  seven hundred and ninety-three thousandth centimeters(math) or as thirty-four point seven nine three centimeters (science). In communicating data in science, it is important to keep it as easily understandable as possible.  How would you read this number....238.619034 kilometers according to how you would read it in math or reading it in science?  Which do you think would be easier to understand or even read?