Surface area and volume, the two most complicated grade 8 math concepts. I spent loads of time trying to wrap my head around calculating surface area and volume for different shapes. But first, before all the math I learned comes into play, I had to design an object that had a variety of different shapes. I and my partner decided to do a blender. I did the bottom half of it while he did the top half of it. We used a cool app called Tinkercad to create it which proved to be a challenge. We also had to use 20 shapes in total. I’m sure you want to see my design so here it is.
I made many different calculations for this project to  calculate the surface area and volume of each shape. Below are all my calculations.
V (blender) = V (hexagonal prism) + V (triangular prism with cutout) + V (left half cylinder) + V (right cylinder) = 31959 + 5997.9 + 2364.7 + 218.7 = 40540.3
V (triangular prism with cutout) = V (triangular prism) – V (cutout) = 5997.9 – 2746.2 = 3251.7
V (cutout) = V (half pyramid at top) + V (triangular prism at bottom) = 1050.7 + 1695.5 = 2746.2
b (half pyramid at top) = b (triangular prism at bottom) = b(triangular prism)= 39.8
h (half pyramid at top) = h (triangular prism at bottom) = 22 – 10 = 12
l (half pyramid at top) = 13.7 – 7.1 = 6.6
l (pyramid at top) = l (half pyramid at top) * 2 = 13.2
w (triangular prism at bottom) = 7.1
h (triangular prism) = 22
w (triangular prism) = 13.7
V (half pyramid at top) = V (pyramid at top)/2 = l(pyramid at top) x b(half pyramid at top)x h(half pyramid at top)/ (3*2) = 13.2 x 39.8 x 12 / 6 = 1050.7
V (triangular prism at bottom) = b(triangular prism at bottom)x h(triangular prism at bottom)x w(triangular prism at bottom)/ 2 = 39.8 x 12 x 7.1 / 2 = 1695.5
V (triangular prism with cutout) = b (triangular prism) * h (triangular prism) * w (triangular prism) / 2 = 39.8 x 22 x 13.7 / 2 = 5997.9
V (hexagonal prism) = 31959
V (left half cylinder) =
V (right cylinder) =
________________
A (blender) = A (hex prism) + A (triangular prism with cutout) + A (left half cylinder) + A (right cylinder) = 5193.8 + 1077.5 + 783.2 + 243.8 = 7298.3
A (hex prism) = 2*A(hex bottom) + 6 * A (hex side) = 2 * 1459.3 + 6 * 379.2 = 5193.8
A (hex bottom) 1459.3
A (hex side) = a(hex prism) * h(hex prism) = 23.7 * 16 = 379.2
A (triangular prism with cutout) = A (triangular prism) – A (cutout) = 1722.3 – 644.8 = 1077.5
A( triangular prism) = 2 * A(side) + A(bottom) + A(back) = 2*(22*13.7/2) + 22 * 39.8 + 39.8 * 13.7 = 1722.3
A(cutout) = A(back) + A(top triangle cutout) = 39.8 * 13.7 + 99.5 = 644.8
A(top triangle cutout) = b*h/2 = 39.8 * 5 / 2 = 99.5
h(top shadow) = hypothenus(triangular prism) = hypothenus(remaining prism) =
V (left half cylinder) =
—
A(right cylinder) = 2*A(bottom) + A(side) = = 243.8
Total SA = 7298.3
Total V = 40540.3
Total V to SA ratio = 40540.3/7298.3 = 5.6/:1
Most of these calculations were very easy except one for the triangular prism. For the triangular prism, there is a cutout from it because some of the hexagonal prism overlaps it. So, I calculated a pyramid at the top of the hexagonal prism overlapping part and below it, a triangular prism volume, then added them together after that I subtracted it from the original triangular prism’s volume. For the surface area, I calculated the area of the triangle that overlaps the triangular prism. This took a very long time and was very complicated, saying this, it is only graded 8 level. The circled part is the triangular prism
Using all of the calculations I started my presentation. It was a non-script presentation using keynote a slideshow app. I made a slide show together with my friend his blog will be linked at the bottom. I introduced what we did then he explained his part then I explained mine. In mine, I added. A slide per shape all of the calculations of that shape and a description of the shape and what it represents on my blender. After that, I had a slide about my driving question which was “how can I maximize a blender for maximum volume?” I can do this by using all the volume to have more things like dashboard batter, buttons, and more. After that, I had a slide with my total surface area and volume and the volume to surface area ratio. Which are Total SA = 7298.3 Total V = 40540.3 Total V to SA ratio = 40540.3/7298.3 = 5.6:1. After all of this, I think my presentation was really good. My presentation here.
I used the core competency’s communication, critical thinking, and creative thinking. I used creative thinking all through my project while making the design I used it to make a blender and to make my slide show. Also, I used creative thinking to figure out a way to calculate the surface area and volume of a non-shape. I used critical thinking to calculate the surface area and volume of all the shapes and I also used communication to make a slideshow with my partner that didn’t interfere with each other’s slides.
In the end, I took all of the things I learned while studying into my slideshow. I really learned a lot and I think this was one of my favourite projects. Thanks for reading and reading my friend’s blog bye.
My friend’s blog