zienic

All pictures without a link were created by me.... __Objectives of 7.1:__
Explore ratios of surface area and volume Develope the concepts of the maximum volume to min surface area

Surface Area Formula.....
SA=2(LxW)+2(WxH)+2(LxH) or for a cube S=6s²

Volume Formula.....
V= LWH or for a cube V= S³

Ratio of Surface Area to Volume.....
The ratio of Surface area to Volume is just the surface area/volume For Eample:

You have this cube that is 4 tall 6 wide and 2 in length and you have the question "For the given cube that is 4x6x2 find the surface area, volume, and surface area to volume ratio." This is how you would find the Surface Area SA=2(LxW)+2(WxH)+2(LxH) SA=2(2x6)+2(6x4)+2(2x4) SA=2(12)+2(24)+2(8) SA=24+48+16 SA=88² units This means that the surface area of this figure is 88² units if the dimentions were 4x2x6. next the volume V=LWH V=4x6x2 V=48³ units this means that the volume of this cube is 48³ units if it had the dimentions of 4x6x2 therefore, the surface area to volume ratio would be 88/48 or 1.8

Class room extends.....
Maximum volume...... In class we disscussed how to find the volume the question that was proposed was.... "If your mom and dad gave you a jar of coins and a peice of paper and told you that they would give you the amount of the money that you can fit in the box." To find the max volume you must cut a 1x1 in square out of the sides of the paper and find the Volume(LWH),the one with the biggest volume will have the must money. To find this we made a table as this: Why it is now 9 instead of 10 is because you took a 1x1 in square from each side as in this example: So sense you cut two 1x1 in squares from 11 and got 9 and the is 11-2=9 then you do that also for the width or 8.5 so 8.5-2=6.5. To get the height you look at the side length of the sqare with in this case is 1. Now you cut a 2x2 in square from each side of the square.(Use same example but 2x2 in squares instead of 1x1) so the equation will be 11-4 because two 2x2 in squares coming from each side would four. 11-4=5 and 8.5-4=4.5...use this same formula for all numbers.
 * Side of square, || length l || width w || height h || volume lwh ||
 * 1 || 9 || 6.5 || 1 || 58.5 ||
 * 2 || 7 || 4.5 || 2 || 63 ||
 * 3 || 5 || 2.5 || 3 || 37.5 ||
 * n || 11-(nx2) || 8.5-(nx2) || n || 11-(nx2)x8.5-(nx2)x1 ||

For further explination of surface area and volume of cubes and rectangular prisims go here: [|CLick me] Then click one of the three link at the left side of the top of the page the will read: Volume Surface Area Cube

To 7.2 click here...