Spreadsheet
Here is a spreadsheet assignment the students found informative. Start with the edge of a cube and let the students increase it in unit increments. Let the students find the Area and Volume and the Ratio of the Volume to area. Then put the data into a graphing program. The most interesting graph is the area and volume together as a function of the edge. Students will see they both increase but the Volume increases a lot faster than the surface area. This shows that large junks of matter have a small surface area compared to their size. It explains why crushed ice is better to cool drinks and why babies have to be protected from a cool environment compared to adults. The volume increases at a faster rate than the area. It shows nice on a graph.
|
Edge |
Area |
Volume |
Ratio |
|
1 |
6 |
1 |
0.166666666667 |
|
2 |
24 |
8 |
0.333333333333 |
|
3 |
54 |
27 |
0.5 |
|
4 |
96 |
64 |
0.666666666667 |
|
5 |
150 |
125 |
0.833333333333 |
|
6 |
216 |
216 |
1 |
|
7 |
294 |
343 |
1.16666666667 |
|
8 |
384 |
512 |
1.33333333333 |
|
9 |
486 |
729 |
1.5 |
|
10 |
600 |
1000 |
1.66666666667 |
|
11 |
726 |
1331 |
1.83333333333 |
|
12 |
864 |
1728 |
2 |
|
13 |
1014 |
2197 |
2.16666666667 |
|
14 |
1176 |
2744 |
2.33333333333 |
|
15 |
1350 |
3375 |
2.5 |
|
16 |
1536 |
4096 |
2.66666666667 |
|
17 |
1734 |
4913 |
2.83333333333 |
|
18 |
1944 |
5832 |
3 |
|
19 |
|
|
|