Rectangular Prism, also known as Cuboid (the shape), is a solid 3D (3-dimensional) object which has six faces, Top, Bottom, Left, Right, Front and Back. Each opposite faces of a rectangular prism are equal, for example Top is equal to Bottom, Left Side is equal to Right Side, and Front is equal to Back.
ANet is a disasemble box, or an open box. Its very usefull when you want to find the area of each faces.
This is an old voice thread that I have used on my second scribe post. Yes, I have finally changed it to public, sorry for the technical difficulties~. Teeehheeee.
What I Know About Rectangular Prisms ; A rectangular prism is a 3d object that has length, width and height. When its flattened it is called a Net. A net is just how you look at the prism when you open it all up. The net helps you get the surface area. l= length h= height w= width
To get the surface area you can find the area of all the parts (top, bottom, front, back, left side and r side) then add them all up. The easier way is to use formulas. The formula for top and bottom is: LxWx2. The formula for front and back is: LxHx2. The formula for the two sides is: WxHx2.
After you find the area for those you add them all after. After you add them you have you're surface area. The surface area is usually cm² or something².
Another thing I learned was to get the volume. The volume for formula is LxWxH or BxH. The B stands for Base and the H stands for Height.
Today in class we learned about the circles and its radius, diametre, and circumferance. Later on during class we also learned how to find the area of a cylinder.
All about the radius and diameter : In class we were told that radius is the distance from the centre of the circle to the edge and you can get it by dividing the diameter because the diameter is double the distance of a radius going from one edge of the circle to the other. The formula to get the diameter : d=2r. meaning the diameter = 2x the radius.
The circumference :The circumference is the distance around a circle. You can get this by 2Pi r (2 x pi x r) pi 2r or pi x diameter.
Cylinder :In class we learned how to make a net of a cylinder. >PLEASE DO NOT DRAW A PEN15< also make sure that the circles are the same size.
L = Circumference W = Height
FORMULA A = Pi R2 C = Pi D A = 3.14 x 5cm2 C = 3.14 x ??cm A = 3.14 x ??cm C = 3.14 A = ??cm2
I have learned about length, width and height of a rectangular prism. I have also learned that you can open it up to make it flat. It is called a net! Each side still is the length, width, and height. l=length h=height w=width
To find the surface area you have to add up all the sides squared. If you had a 2x2x3 prism, you would have to multiply..
LxHx2 LxWx2 HxWx2
LxHx2 is the front and back of the prism. LxWx2 is the top and the bottom of the prism HxWx2 is the left side and right side of the prism.
After you add it up you should have the surface area. To find the Volume of a rectangular prism, you can just do Length x Width x Height! Volume is how many cubed (insert measurement here example cm) can fit inside the prism.
If the length = 2cm width = 2cm height = 3cm
You would do 2cm x 2cm x 3cm to get the volume The volume would be 12cm cubed.
What I know and learned about rectangular prisms: We learned about getting the Surface Area and Volume of rectangular prisms. But the step we always do is making a Net. Surface Area: There is a lot of work to do before you can actually find out the surface area. You have to find out the area of each of the shapes. The top, front, and the left side. You only need to find out only one of each shape because each one has a pair. The right and left sides, the front and back, and the top and bottom.
The formula for figuring out the top and bottom is LxW (length x width). Since you only need to find out one of each shape all you have to do is then multiply it by 2. So it would be lxwx2 to equal the answer with a exponent of 2 (squared). E.g 3cm x 2cm x 2 = 12 2 cm.
The formula for figuring out the sides is HxW (height x width). Again, since you only need to find out only one side all you have to do is multiply it by 2. So then it would be hxwx2 to equal the answer with an exponent of 2 (squared). E.g 6cm x 2cm x 2 = 24 2 cm. The formula for figuring out the area for the front and back is HxL (height x length). Since you only have to find out one of the shapes all you have to do is multiply the first answer by 2. So then it would be hxlx2 to equal the answer with an exponent of 2 (squared). E.g 6cm x 3cm x 2 = 36 2 cm.
Then you add all the numbers to together to get the total surface area. The exponent for surface area is always 2.
Volume: Figuring out the volume for a rectangular prism is some what harder that find the surface area. But in some ways it is easier because you are only figuring out what is the number of the inside of the shape. There are two formulas of finding the volume.
Area of the base x Width is one of the formulas. First you find out the measurement of the base. Then you multiply that by the width because that is how many base numbers you have. E.g Base number = 15 cm 2 and the width = 3 cm. So it would be 15 cm 2 x 3 cm= 45 cm 3.
The second formula is LxHxW (length x height x width). You first find out the measurement of the length, width, and the height. Once you do then you multiply them all together. E.g L = 5 cm H = 10 cm W= 3cm. 5cm x 10 cm x 3 cm = 150 cm 3.
In class we learned how to find the surface area/ volume/ & net of squares and rectangular prisms.
Net:
A net is a picture of a 3 dimensional object flattened out so you are able to view all sides n one dimension.
E.G:
The yellow shaded parts in the picture reps. the sides of the rectangle. The black shaded parts represent the top and bottom of the object and the blue shaded areas rep. the back and front. These colors also rep. that they are the same measurements. (e.g the yellow shaded areas are both 5 cm ) this will help you to find the surface area and volume later on.
Surface Area:
To find the surface area of a rectangular prism if you find the area of each side on the net all you would have to do is add up each side and get the surface area of a rectangular prism.
E.G:
( 8 + 8 + 12 + 12 +10 + 10= 60 cm (squared) )
Volume:
When finding the volume of a rectangular prism all you have to do is : [ Length X Width X Height ] measurements.
E.G:
As you can see all of these problems are easy to solve when you ahve a net and the measurements of the object.
A rectangular prism is a 3D(Three Dimensional)object that has sides called Height, Length, Width and it looks something like the picture below.
A rectangular prism has 6 faces and those faces are called Top, Bottom, Front, Back, Left Side and Right Side. We can see all 6 faces when we make a diagram called the Net. The Net is just a diagram showing what the rectangular prism would look like if you opened it up and flattened it out. The Net on the left shows all 6 faces and which ones they are and the Net on the right shows what each side is(Height,Length,Width). The Net helps you find the surface area of the prism.
What a Cube is
A cube is basically the same thing as a rectangular prism but the Height, Length and Width are all equal.
Just like the rectangular prism the cube also has 6 faces. The nets are also similar but the only difference is the sides in the cube are all equal. The net of the cube also helps you find the surface area.
How To Find The Surface Area of a Rectangular Prism/Cube
One way of finding the surface area is to divide them into groups and find their areas separately then add them all together. The groups you divide them into are Front/Back, Top/Bottom and Sides(L Side and R Side) because they are both equal and it makes life easier. There are different formulas for each group.
The formula for finding Front/Back is Area=2(Height X Length) or A=2(H X L)
The formula for finding Top/Bottom is Area= 2(Width X Length) or A=2 (W X L)
The formula for finding Sides is Area= 2(Width X Height) or A=2 (W X H)
The 2 is there because after you're done answereing the brackets you multiply what you got in the brackets by 2. After you find those you add them all up to get the surface area.
The other way to find surface area is to add all the sides up, but that way takes too long.
How To Find The Volume of a Rectangular Prism/Cube
To find the volume you can use the formula Length X Width X Height. The formula says it all so i don't think I need to explain it.
The other formula is Base X Height. The Base is usually either the Top or Bottom. This formula is also simple so I won't explain it.
Solving The Surface Area and the Volume of a Rectangular Prism/Cube
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.
1st: find the area of the top and the area of the bottom. LxW. 2nd: find the area of the front and back. HxL= 3rd: find the area of the left side and right side. HxW=
We learned how to find the surface area of a rectangular prism and this is how:
First you need to make a net which is a rectangle that is flatten out where you'd be able to see all of the sides, like this.
The colours represents which are the same which is found across from each other.
(Eg. Red is the same as the Red across from it.)
Now measure each side to find how many centimetres that part has. You can just measure one part of each colour since they're all the same. Measure for Height, Length and Width. Once you get the measurements, multiply by 2 to represent the second part of that colour. (Since their are 2 colours that are the same for the same parts.)
Next add everythingtogether to get the surface area!
Volume of Rectangular Prism
Finding the volume is really not such a big deal! Actually, all you have to do is take the measurements of the Length, Width, and Height and multiply them together! Easy right?
Same goes for when you're trying to solve a cube!
Make a net like you did on the rectangular prism!
Finding the surface area of a cube is really easy!! A piece of cake and I'll show you how!
A cube has all of the sides equal which means you just have to measure one side and that measurement goes for the Length, Width, and even Height!
VOLUME!
Same goes for volume! It's just like how we did with the rectangular prism.
Hope you guys find this understandable! (especially the colour thingy part! XP)
First you take your rectangular prism and flatten it so you can see all the sides. This is called a net: Now take the measurements for the height, width and length or each part of the net (top & bottom, left/right side, front & back) and find the area of each. Since the top-bottom, sides and front-back are the same, you only need to measure one part (top, left side and front) then multiply what you get by 2 to represent the bottom, right side and back.
Then you add everything together. There's your surface area. It should look something like this:To find the volume of a rectangular prism, all you need to do is take the length, width and height measurements then multiply them together. Here's an example:Well... I'm done.
For the past 2 weeks, we learned how to find surface area's and volumes of 3-dimensional (3D) objects like rectangular prisms and cubes. Here is how to find the Surface area and Volume of a Rectangular Prism:
Surface Area of a Rectangular Prism
This is a Rectangular Prism. You can see the length, width, and height from any angle, meaning it is a meaning it is a 3D object.
Surface area is "how much wrapping you need to cover the whole object". So, if you were to cover it, you much wrapping would you need in a unit of measurement (not squared).
Our new Rectangular Prism has some measurements attached to it, so we can solve the surface area and Volume.
So: Length = 6 cm Width = 10 cm Height = 6 cm
There is 1 formula for finding surface area:
-It is (Area of L side + Area of R Side) + (Area of Top) + Area of Bottom) + (Area of Front + Area of Back)
One important thing must be done to simplify finding the surface area. You must turn the rectangular prism into its 'Net' form, which is as follows:
Now do the equation (Since L side and R side, and Top and bottom, and Front and back have the same area, simply x2 to use less space.:
Surface Area =(Area of L side x 2) + (Area of Top x 2) + (Area of Front x 2)
=(60cm² x 2) + (36cm² x 2) + (60cm² x 2) =(120cm²) + (72cm²) + (120cm²)
=312cm² is the Surface Area
Now Volume is pretty easy, there are 2 different ways on finding it. One is : Length x Width x Height the other one is Area of Base x Height
I'll do both to prove they both work: The measurements are: L = 6 cm W = 10 cm H = 6 cm
The Formula: = Length x Width x Height = 6cm x 10 cm x 6 cm = 60 cm x 6 = 360 cm³ (note, the answer is CUBED or the power of 3 (³) because you are multiplying 3 dimensions together: length, width, and height)
The Second Formula is Area of Base x Height: Area of Base = L x W or L x H or W x H Area of Base = L x W (for now) Area of Base = 6cm x 10cm Area of Base = 60cm²
Height = 6cm
60cm² x 6 = 360 cm³
See, the answer is 360cm³ for both, meaning they both work. The Length x Width x Height one is easier, in my opinion, because it takes less work to do. And that's how you find the volume and surface area of a Rectangular Prism.
Kiahna's Bob Everything You know about Rectangular Prisms Surface area of A Rectangular Prism To figure this out you have to cut the box in half like so! insert pic
then you have to do a formula for each side! For the Front and the Back of the Box you have to use this formula Hieght x Length = ?? For the Right side and the Left side of the box you have to use the formula Height x Width = ?? For the bottom and top you have to use the formula Length x Width = ?? then for each of them yuo multiply it by two and that is your answer Now that we know all of this lets give out the numbers Hieght is 10cm the Length is 5cm and the width is 2 cm. so lets figure it out Font and Back side: h x L = 10cm x 5cm x 2 = 100cm Right and left side: H x W = 10cm x 2cm x 2 = 400cm Bottom and Top: L x W = 5cm x 2cm x 2 = 100cm
Now you add it all together to get the surface area 50cm+20cm+10cm= 80cm²
BubbleShare: Share photos - Powered by BubbleShare
Volume of a Rectangular prism
to find the volume you have to do length x width x hieght =
or you can do base x hieght =
so the measurments are length 3cm height 5cm width is 1cm
Volume of Rectangular Prism
VOLUME!
Hope you guys find this understandable! (especially the colour thingy part! XP)
