7B Math: Efficiency Expert Portfolio
Directions:
You will mathematically and experimentally show how 4 figures made from the SAME size paper will produce different volumes.
Take 4 sheets of paper, you will use 8x10 in 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.
A: B: C: D:
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 provide the volume of each shape A,B,C and D using 8x10 in paper. USE PROPER UNITS FOR VOLUME. The 4 volumes with units is ALL YOU HAVE to provide. No pictures needed.
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!
Paper dimensions ( length and width, you may use 8x10 inches) You may NOT use the 8 ½ x 11 inches I used.
Volumes (use correct unit) of tall prism A, short prism B, tall cylinder C and short cylinder D.
hint: in the example my paper is 8 ½ x 11 in our volume will be in³
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.
Assuming the paper dimensions are 8x10 inches,
A: Tall rectangular prism
length = 8 inches
width = 2 inches (1/4 of 8 inches)
height = 10 inches
Volume = 8 x 2 x 10 = 160 cubic inches
B: Short rectangular prism
length = 2 inches (1/4 of 8 inches)
width = 8 inches
height = 10 inches
Volume = 2 x 8 x 10 = 160 cubic inches
C: Tall cylinder
radius = 1.75 inches (half of the diameter)
height = 10 inches
Volume = 1.75 x 1.75 x 3.14 x 10 = 96.625 cubic inches
D: Short cylinder
radius = 1.75 inches (half of the diameter)
height = 2 inches (1/4 of 8 inches)
Volume = 1.75 x 1.75 x 3.14 x 2 = 19.325 cubic inches
why do you devide it by 1/4?
Because the task requires us to make figures out of the same paper, and the paper dimensions are 8x10 inches. To create different shapes, we need to use the same amount of paper for each shape. If we divide the paper length or width by 4, we get a quarter of the paper dimensions, which allows us to create four different shapes using the same paper.
To find the volumes of the four shapes (A, B, C, and D) using the 8x10 inch paper, you need to follow the given instructions and formulas.
1. For the tall rectangular prism (shape A):
- Divide the length (8 inches) by 4 to find the measurement of the height.
- Divide the width (10 inches) by 4 to find the measurement of the base.
- Use the formula for volume of a prism: Volume = length x width x height.
- Substitute the obtained measurements into the formula and calculate the volume.
- Provide the volume with the correct unit (cubic inches).
2. For the short rectangular prism (shape B):
- Follow the same steps as for shape A but using the short dimensions instead.
- Divide the shorter length (8 inches) by 4 to find the measurement of the height.
- Divide the shorter width (10 inches) by 4 to find the measurement of the base.
- Calculate the volume using the volume formula for prisms.
- Provide the volume with the correct unit.
3. For the tall cylinder (shape C):
- Find the diameter of the circle top by dividing the known circumference (11 inches) by 3.14.
- Divide the diameter by 2 to find the radius.
- Substitute the radius and the given height into the formula for the volume of a cylinder: Volume = radius x radius x 3.14 x height.
- Calculate the volume and provide it with the correct unit.
4. For the short cylinder (shape D):
- Follow the same steps as for shape C but using the short dimensions instead.
- Divide the shorter diameter by 2 to find the radius.
- Calculate the volume using the volume formula for cylinders.
- Provide the volume with the correct unit.
Remember to provide the volumes of all four shapes (A, B, C, and D) with the proper units (cubic inches) as requested.