🔥PORTFOLIO FOR CONNECTIONS ACADEMY🔥
You will mathematically and experimentally show how 4 figures made from the SAME size paper will produce different volumes.
Take 4 sheets of paper (I used 8 ½ x 11 printer paper….you cannot use 8 ½ by 11 in but can use 8x10 in paper instead) and create:
​-A: tall rectangular prism
-B: short rectangular prism
-C: tall cylinder
-D: short cylinder
Mathematically you will figure the dimensions of your shapes just using your paper dimensions versus a ruler.
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A: ​​​​B: ​​​​​C: ​​ D:
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Volume of Prism: l x w x h
Volume of Cylinder: r x r x 3.14 x h
So we will use our paper dimensions to find the shape measurements needed to find the volume of each one.
A and B….the prisms are easy. We just take the dimension and divide it by 4 to find our measurement.
C and D ….the cylinders are a bit more tricky. We know the circumference of our circle tops and the heights of our cylinders but we need to find the radius of our circle top.
Circumference = diameter x 3.14
11 = d x 3.14
Divide both sides by 3.14 to find the diameter
11/3.14 = d
3.5 = d but in finding volume of cylinder we need the radius.
d/2 = r 3.5/2 = 1.75 in
You will proved the volume of each shape A,B,C and D
OPTIONAL: Now you can test your volumes by actually making these open ended paper shapes and filling them with rice or beans or some material to figure out which one holds the most. It is best to make your shapes out of a thicker paper but I understand if you don’t have thicker paper.
Here is what I need for full credit!
1. Paper dimensions ( length and width)
2. Predictions.
a. Will prisms A and B hold the same?
b. Will cylinders C and D hold the same?
c. Will tall prism A or tall cylinder C hold the same?
d. Will short prism B or short cylinder D hold the same?
3. Volumes (use correct unit) hint: if paper is 8 ½ x 11 in our volume will be in³
4. The experiment portion (filling your open ended shapes with rice or beans to see which holds the most) is OPTIONAL but is a fun, hands on way to support your math.
5. Label A,B,C and D as Small, Medium, Large, and Extra Large based on their volumes.
To mathematically and experimentally show how 4 figures made from the same size paper will produce different volumes, follow these steps:
1. Start with 4 sheets of paper (preferably thicker paper, but regular printer paper will work).
2. Cut each sheet of paper according to the following dimensions:
- For the tall rectangular prism (A), divide the length and width of the paper by 4 to find the measurements.
- For the short rectangular prism (B), also divide the length and width of the paper by 4.
- For the tall cylinder (C), you need to find the radius of the circle top. Since you know the circumference of the top, which is the same as the width of the paper (11 inches), divide it by 3.14 to find the diameter (d). Finally, divide the diameter by 2 to get the radius (r).
- For the short cylinder (D), follow the same procedure as in C to find the radius.
3. Once you have the dimensions for each shape, you can calculate their volumes using the formulas provided:
- The volume of a prism is calculated by multiplying its length, width, and height (l x w x h).
- The volume of a cylinder is calculated by multiplying the radius squared, the height, and 3.14 (r x r x 3.14 x h).
4. Plug in the measurements you obtained from dividing the paper dimensions and calculate the volumes of each shape.
5. You can make the experiment portion optional by filling each open-ended shape with rice or beans to see which one holds the most. This is a hands-on way to support your math calculations and predictions.
6. Finally, label each shape (A, B, C, D) as Small, Medium, Large, and Extra Large based on their volumes.
Here is what you need for full credit:
1. Paper dimensions (length and width).
2. Predictions:
- Will prisms A and B hold the same?
- Will cylinders C and D hold the same?
- Will tall prism A or tall cylinder C hold the same?
- Will short prism B or short cylinder D hold the same?
3. Volumes (use the correct unit, in this case, in³).
4. The experiment portion (optional) where you fill the shapes with rice or beans to see which one holds the most.
5. Label shapes A, B, C, and D as Small, Medium, Large, and Extra Large based on their volumes.