Finding the Density of an regular shaped object.

The Density of an Object Method

            Density of an object is more important than you might think.  Have you ever seen how some people can float in a pool without even having to move a muscle while others have to move to stay afloat?  Have you been able to float in the ocean better than you can float in the pool?  This is all about density.  Why is it that most rocks sink in water while pumice rock floats very well in water?  How can a silver dollar coin float on liquid mercury?  Again, it is all about density.  Why does cold air sink and warm air move up?  Why does granite rock carry seismic waves better than sandstone?  Why will salt water remain at the bottom of a beaker below freshwater in the same beaker?  Why does cold water sink and warm water rise.  Guess what?  It is all density!

            In my years of teaching sixth grade science, students had a hard time of understanding density.  So they were introduced to it in my classes.  There are two ways to find density: for objects that you can measure with a metric ruler.  These were regularly shaped objects that have a length, width, and height; and the other was using a graduated cylinder and water as part of the process to find the density.

            Now density is described as the relationship of an object’s mass in grams to it volume in milliliter or cubic centimeters.  This above named mass and volume units would be larger for big objects.   Such as kilograms or liters.  Now rereading the definition of density, you may have a questioning look on your face.  I know my sixth graders did.  So we discussed it a lot.  In this case what we were trying to understand was this.  So if I have 1 cubic centimeter piece of something; that 1 cubic centimeter of that something would have a certain mass.  In other words…say you have an object that has a volume of 1 cubic centimeters and its mass is 2 grams. 

            Here is where the math comes in.  The equation for calculating density is: density is equal to the mass of the object divided by its volume.

D= mass divided by volume

D= M/V

So density is equal to 2 grams divided by 1 cubic centimeter

D= 2 grams/1 cubic centimeter

D= 2g/1 cm³

D= 2g/cm³  (2 grams per cubic centimeter)

Therefore each cubic centimeter of that object will have a mass of 2 grams.

The object’s density is 2 grams per cubic centimeter.

1.                   If an object has a mass of 10 grams and a volume of 5 cubic centimeter, what is its density?  Remember to divide the mass by the volume and the units in the answer are grams per cubic centimeter.

D= 10g divided by 5 cm³.  10 divided by 5 = 2   D= 2 g/cm³

2.                  If a rock has a mass 25 grams and a volume of 5 milliliters, what is its density?  Remember to divide the mass by the volume.  Your answer will have the units of grams per milliliter.

3.                  This object has a volume of 50 mL and a mass of 400 g.  What is its density?   Remember your units will g/mL.

Finding Volume of a block of wood

1.                  You will use a metric ruler that is correct for what you are going to measure.  In this case a 30 cm metric rulers works very well.

2.                  You will be measuring the block’s length (longest side), them width (next longest side), and finally the block’s height or thickness.

3.                  You will measure to the tenth of a centimeter also known as 0.1 centimeters.  Be sure to record what you  have written down what you measure on a data chart to a tenth of a centimeter.

4.                  First measure the length.  Refer to the picture below.

a.      This measurement is 14.8 cm

5.         Now measure the width of the block in centimeters.  

Refer to the picture below.

            a.         This measurement is 4.4 cm.

6.         Finally you will measure the height or thickness of the block.  

Refer to the picture below.

            a.         The measurement is 1.8 cm.

7.         Now you are ready to use the math formula of Volume is equal to the                   length times the width times the height.  It can be written this way:
           V=LxWxH.

            a.         First multiply 14.8 times 4.4

                                                               14.8

                                                              X4.4  

                                                                582

                                                            +582 

                                                              6512

            b.         Now multiply 6512 by 1.8.

                                                              6512

                                                              X1.8 

                                                            52096

                                                          +6512

                                                         117.216   cubic centimeters       

c.         But for a scientist this is not the final answer.  For scientific                                    accuracy the answer can only be as accurate as the measurements                          which in this case are only accurate to one decimal place or 0.1                              cm.

d.         Using your math skills in rounding, you will round the above answer                     to one decimal place or 0.1 cm.

                    i.          Looking at the answer: 117.216 the 6 digit is greater than 5                                   so the 1 to the left is rounded up to a 2.  But since the 2 is                                       less than 5 the .2 digit is not affected and stays a 2.

e.         Therefore the final answer for a scientist is 117.2 cm³   
            This answer tells other scientists that the measurements to find the
            volume of the block were only made to a tenth (0.10 of a centimeter.

8.         The next part is the measure the mass of the block of wood in grams 
            using a balance or digital weight device.  Again the mass is measured to a
            tenth (0.1) of a gram.  Hopefully you already have been trained to use
            that equipment.

            a.         The mass of the block is 58.8 grams.

9.         The formula for calculating density is:  Density is equal to the mass of the
            object divided by its volume.

            a.         D=M/V

10.       In this problem you will be dividing a larger number (divisor) into a
            smaller number (dividend).  This means you will have a zero point (0.)
            some number answer (quotient).

a.         In this math process you will divide 117.2 cm³ (divisor) into 58.8 g (dividend).  Remember your quotient will be less than 1.  Meaning you will start with a 0. then a number.

b.         When 58.8 g (dividend) is divided by 117.2 cm³ (divisor), your answer will be:

            0.5017064846 g/cm³

c.         This answer is not yet finalized.  Look at the number of decimal places your measurements were made to.  As you can see it was only 0.1.  This means your answer can only be accurate to a tenth or 0.

d.         So you round your answer to 0.5 g/cm³.

11.       Your final answer for the density of this block of wood is 0.5 g/cm³.

QUESTION:

If the density of distilled water is 1.0 g/ml, and 1 cm³ is equal to 1 mL; will this block of wood sink or float in distilled water?