What happens to the surface area and volume of a 3-D figure when the demensions change???

When the demensions of a figure are enlarged or they become smaller, the volume and surface area of the figure will change. For example, if you multiply the demensions of a figure by three, the volume of the figure will be three times bigger. If you devide the demensions by two, the volume of the figure will be two times smaller. The surface area will also become larger or smaller, but it is not as easy to figure out as the volume where it would just be three times bigger or two times smaller. A trick to find the surface area is to use what I call the "Y" trick. You draw a Y and then you put the demensions at the end of each line. In between 2 of the numbers, multiply them together. After that, multiply that number by 2. Do that all 3 times and then add all the answers together. This final answer will be your surface area. When you find out the surface area of the original figure... you need to find the surface area of the new demensions and compare your answers by deviding the surface area of the new figure by the surface area of the original figure. This would be how much bigger the new figure is compared to the original figure.You should do the oposite if you made the figure smaller.

e.g. To find the volume of a figure, you multiply length, by depth, by height. If the size of the demensions of a cube is 2x2x2, and you need to multiply each demension by 3, then the new demensions would be... 6x6x6 (or 2x3 by 2x3 by 2x3.) The new demensions are now 3 times bigger than the original demensions so the figure's volume is three times bigger. You need to find the surface area of both figures (original and new) and then you need to compare them by deviding the larger number by the smaller number. This is how much bigger or smaller the original surface area is compared to the new surface area! Here is an example below...

SAexample.jpg

SAexample1.jpg

These things are useful in variouse jobs and other things in life so I hope that you learned something new by reading this page!!! Bye! There is a quiz below to see if you learned the facts of this page.

QUIZ:
1) How do you find the volume...
2) What do you use to find the surface area...
3) What do you do to find how much the surface area and volume have changed between a new and original figure...
4) If the demensions of the figure are 3x3x3, then what is the volume...
5) If the demensions of the figure are 3x3x3, then what is the surface area...
6) If the demensions of the new figure are 6x6x6, then what is the volume...
7) If the demensions of the new figure are 6x6x6, then what is the surface area...
8) What is the difference in the volume between the new figure and the original figure...
9) What is the difference in the surface area between the new figure and the original figure...


ANSWERS:
1) base x depth x height
2) the "Y" trick
3) you divide the surface area/ volume of the new figure by the surface area/ volume of the original figure
4) 27
5) 54
6) 216
7) 216
8) 8 times difference
9) 4 times difference