Student Information

Your teacher may want you to print the worksheet for this assignment.

You will be extending your exploration of the relationships among the volumes of cylinders, cones and spheres of the same radius.  In class, you have already experimented with how much larger a cylinder is than a sphere and how many full cones it takes to fill a cylinder.  In this lesson, you will be using the Excel spreadsheet to mathematically make these comparisons.

The spreadsheet has the formulas already inserted to calculate the volume and the ratios.  You need to fill in values for the radius and the height.  Remember, these values have to be greater than zero.  If you put in a negative number, it will show up in red.  If you put in zero, nothing will happen.

The spreadsheet has been started for you.  You will need to open it and save it to your folder on the H drive.  You can do this by going to File, Save As.  Once you are in your folder on the H drive, save the spreadsheet as volume.xls.  Change the size of this page to fit half the screen.  Change the size of the Excel spreadsheet to fit the other half of the screen.  You can do this by moving your mouse to the sides of the page and dragging the two sided arrow to make the page larger or smaller.

Spreadsheets have cells named A1, A2, A3, A4, . . .   Letters name the columns and numbers name the rows.

            A         B          C         D         E          F          G         H         I           J           K

1

2

3

4

5

6

7

To write text, just type.  But to write math formulas use “ = “  sign first then the formula.

Example, to type area of a rectangle, type    = l* w.

Type the following text:

In cell B2 type the formula for volume of a cylinder.   V  =   ח r ²  h

In cell A3 type “Radius.”                  In cell B3 type        2

In cell A4 type “Height.”                  In cell B4 type       10

In cell A5 type “Volume.”                 In cell B5 type     = 3.14*(B3*B3)*B4

Your paper will look like the following:

            A                     B                      C                     D                     E                      F         

1                                 

2                                   V = ח  r ²  

3    Radius                    2

4    Height                    10

5    Volume                  125.6       (This is the volume for the cylinder with radius 2 and height of 10.)

6

7

Now type Cylinder in cell B1

1.  You will find the volume of the sphere and cone with radius of 2 and height of 10.

      Type the word Cone in cell D1

      Type word Sphere in cell F1

      In cell D2 type the formula for volume of a cone.                             (V= 1/3  ח  r ² h)

      In cell F2 type the formula for volume of a sphere                            (V= 2/3  ח  r ² h)

      In cell D5 type the equal sign, 1/3 “times”3.14 “times” the cell where the radius is “times”  the cell  with the radius “times" the cell where height is        located.  (=1/3*3.14*(B3*B3)*B4)

      Then hit the return.                           

      What happens?

      Use the same procedures for the volume of a sphere with radius 2 and height 10.

Compare the volume of the cylinder to the volume of the cone.  How many times larger is the cylinder compared to the cone?

Compare the volume of the cylinder to the volume of the sphere.

Compare the volume of the cone to the sphere.  How many times larger is the sphere to the cone?

Enter a variety of values (or those chosen by your teacher) to see if you can explain why the ratios are always the same and explain what they mean in terms of the relationships.  Below are some specific questions to help you make a complete explanation.  Be sure to write in complete sentences!

1.  Find the volume of a cylinder, sphere, and cone with a radius of 3 and height of 3.

2.  Find the volume of a cylinder, sphere, and cone with a radius of 3 and height of 15.

3.  Find the volume of a cylinder, sphere, and cone with a diameter of 6 and height of 3.

4.  Find the volume of a cylinder, sphere, and cone with a radius of 3 and height of 24.

Use your volumes from 1—4 to answer the rest of the questions.

5.  Compare the volume of the cylinder to the volume of the cone.  How many times larger is the cylinder compared to the cone?

6.  Compare the volume of the cylinder to the volume of the sphere.

7.  Compare the volume of the cone to the sphere.  How many times larger is the sphere to the cone?

8.  Save your spreadsheet as volume.xls to your folder on the H drive.  Your teacher will give you directions on how to post it to your technology passport.