A: The dimensions of the paper are 8x10 in, which means the base of the prism will be 8x10 in. To create a tall rectangular prism, the height will be 8 in and the length will be 2.5 in (since 10 divided by 4 is 2.5).
Volume of A: 8 x 8 x 2.5 = 160 cubic inches
B: To create a short rectangular prism, the height will be 2 in (half of 4 paper divisions) and the length will be 5 in (half of 10 paper divisions).
Volume of B: 8 x 5 x 2 = 80 cubic inches
C: To create a tall cylinder, the height will be 8 in (same as paper height) and the diameter will be 2.2 in (circumference of 7 in divided by 3.14, then divided by 2 for the radius).
Volume of C: 1.1 x 1.1 x 3.14 x 8 = 24.78 cubic inches
D: To create a short cylinder, the height will be 2 in (half of 4 paper divisions) and the diameter will be 2.2 in (same as C).
Volume of D: 1.1 x 1.1 x 3.14 x 2 = 7.77 cubic inches
Therefore, the volumes with the proper units for each shape are:
A: 160 cubic inches
B: 80 cubic inches
C: 24.78 cubic inches
D: 7.77 cubic inches
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 (I used 8 ½ x 11 printer 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.
1 answer