Problem Statement: Find out how deep they would have to drill to reach the sandstone, and how thick the sandstone is.
Process: In order to find out how deep they needed to drill I cut the large triangle shape in half and solved it with sin, cos, or tan to figure out the lengths of the opposite and adjacent sides. I added the opposite sides together and got the length that needed to be drilled. Then I also split the width of sandstone into two triangles and used the same steps to find the thickness of the sandstone.
Solution/Reflection: For the length needed to drill my solution was 2.205 miles and the width of the sandstone was 13.211. I think my answer is correct because I got help from Clarice and Dan but this Pow was very difficult for me. I didn’t know how to start the problem and kept getting wrong answers. After Dan explained it to me I understood it better but it was still pretty challenging.
Extension Question: What if there were another layer of sandstone above the one calculated and you had to figure out how far apart those two layers are.
Bees Final
Question: What evidence would convince me that a hexagon is the best shape for a honeycomb?
Octogonal Prism: An activity that helped me understand the idea was the octogonal prism assignment. We had to find the volume of multiple prisms after finding their area and depth.
Formulas:
½ x b x h
Cos, Sin, Tan
Volume= width x height x depth/2
This relates to the central question because we were figuring out which shape would be the best shape for a honeycomb. I had to recognize and resolve some of my errors during this problem because my first answer didn’t look right. I figured out what the problem was, fixed it, then finished the problem.
Shape Tessellations: During this activity we had to draw the same shapes and see if they tessellated or not most shapes did but some did not. We tried multiple shapes to figure out if they would possibly work for a honeycomb. I had to really think about how these shapes would fit together because some didn’t work.
Perimeter of a Shape: We had to find the area and volume of a shape with a certain perimeter. Formulas:
perimeter / amount of lines
This activity relates to the question about bees because we were testing multiple shapes with different perimeters to see which was the best for a honeycomb. I had to recognize my mistakes and fix them, Mason helped me get the hang of it and explained to me what I was doing wrong.
Shape Integrity: We analyzed structural integrity by constructing toothpick and marshmallow 3D shapes, letting them dry, then setting textbooks on top of them to see if they fall over. Some held multiple books and some couldn’t even hold one. I had to come up with my own ideas and listen to others' ideas in order to find out if the shapes were strong enough or changed at all.
Answer: We learned that the octogonal shape is the best for a honeycomb because all of the space is used and the structural integrity is the highest with this shape.