Monday, April 14, 2008

Davids BOB

What I have learned/know about rectangular prisms.
Rectangular prisms are 3 dimensional shapes, and in class we've learned how to find certain things about the rectangular prism. First of all, theres something called the Net, which is just like what the prism would look like if you made it flat.

The next thing would be the measurements of the prism, if you look at the net, you can use that to figure out what the length, width, and height of the prism is. You could switch those numbers around though, because any side of the prism could be the bottom or the base because if you were going to cut it it would be the same on each side. So for our prism lets say we have a length of 8cm, width of 5cm, and a hieght of 2cm.

We can use those measurements now to figure out the surface area of the prism, so how many square cm are in that net. Its kind of broken up into pieces, but the face of the prism thats on the opposite side will always be the same if we're dealing with rectangles and...stuff. First we would want to figure out how large the top, bottom, left side, right side, front and back are. Height x Length is how you would get the front or the back, you would have to multiply your answer by 2 to get the area of both the front and the back. Height x Width is how you get the right/left sides, also multiple by 2 to get the area of both sides. Length x Width, this is how you would find the area for the top or bottom, again, multiply by 2 to get the area for both, if it was a square then all of the sides would be the same so if you found one out you know the rest. When we've figured out the are of each face on the rectangular prism, we need to add them up to get the surface area of the whole prism. We could add each little thing up, or we can do something like this, 2(hxl)+ 2(hxw)+ 2(lxw)=Surface Area
So with our rectangle, the surface area would be something like this:

2cm x 8cm = 16cm x2 = 32cm squared

2cm x 5cm = 10cm x2 = 20cm squared

8cm x 5cm = 40cm x2 = 80cm squared

32cm2 +20cm2 +80cm2= 132cm2

Thats only one way of doing this, and its pretty simple too because we found the area for all the sides before we added them up.
We also learned how to find the volume!

There are two ways we could figure out the volume, one was multiply all of the measurments of a rectangular prism. By that I mean Length x Width x Height, not the cm squared but how many cm it was on the side of the rectangular prism. If the prism had a 8cm length, 5cm width, and a 2cm height, then we could do 8cm x 5cm x 2cm = 80cm cubed (we use a little 3 to represent cubed and we use it to know we're talking about something in 3 dimensions).

You could do the same thing with a cube except you would have different numbers for the length, width, and height. Another thing we could do is Base x Height, your base is usualy the width x length. This solution is a little different though, you can represent it in a different way. But you would find out what the base is first, so usuing the cube again, it would have a base of 40cm squared, multiplying that by the height (2cm) would get us our volume of 80cm cubed. It would look something like this if you wanted to draw it out.

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