My partner and I decided to measure the amount of clay it would take to make a cylinder mug with a hashtag symbol for a handle. All of the measurements we took were in inches and we assumed that the top and bottom sides of the cylinder and the lengths of the hashtag ends were the same.
We were required to use an area formula, a trigonometric function, and a volume formula. So to start taking apart our mug, we started by measuring the cylinder using the formula v(cylinder)=πr^2h. We measured the outside this way and then we measured the inside the same. Then we separated the hashtag (#) into 4 different rectangles and then we used the volume formula v(rectangle)=l*w*h. Since we didn't use a trigonometric function on the original item, we decided to construct a hypothetical cup with a pentagon base and use trigonometry to solve for the base and measure the 6 triangles we split the pentagon into. For the hashtag, we had to account for the four, 1-inch overlaps so we also subtracted that from the total.
A challenge that we faced during this project was the fact that we measured in inches, rather than something smaller like centimeters. We continued measuring in inches to finish the project but once we were finished and had presented we decided that centimeters would have been the better choice of measurement. We were also unsure on how to measure the hashtag at first. We weren't sure if we wanted to do it like we did or if we wanted to find the volume of the whole rectangle and then subtract all the spaces that weren't made of clay. Some Habits of a Mathematician my group used were look for patterns, take apart and put it back together, and stay organized. We took apart the mug and found the volume of the cylinder and then the hashtag and then added them together, we used multiple papers to keep ourselves organized, and we looked for patterns and assumed the volumes of the rectangles after solving for one. If we were to do this project again, we would probably measure something bigger or more difficult, and we'd probably use a smaller measurement, depending on what we chose.
We were required to use an area formula, a trigonometric function, and a volume formula. So to start taking apart our mug, we started by measuring the cylinder using the formula v(cylinder)=πr^2h. We measured the outside this way and then we measured the inside the same. Then we separated the hashtag (#) into 4 different rectangles and then we used the volume formula v(rectangle)=l*w*h. Since we didn't use a trigonometric function on the original item, we decided to construct a hypothetical cup with a pentagon base and use trigonometry to solve for the base and measure the 6 triangles we split the pentagon into. For the hashtag, we had to account for the four, 1-inch overlaps so we also subtracted that from the total.
A challenge that we faced during this project was the fact that we measured in inches, rather than something smaller like centimeters. We continued measuring in inches to finish the project but once we were finished and had presented we decided that centimeters would have been the better choice of measurement. We were also unsure on how to measure the hashtag at first. We weren't sure if we wanted to do it like we did or if we wanted to find the volume of the whole rectangle and then subtract all the spaces that weren't made of clay. Some Habits of a Mathematician my group used were look for patterns, take apart and put it back together, and stay organized. We took apart the mug and found the volume of the cylinder and then the hashtag and then added them together, we used multiple papers to keep ourselves organized, and we looked for patterns and assumed the volumes of the rectangles after solving for one. If we were to do this project again, we would probably measure something bigger or more difficult, and we'd probably use a smaller measurement, depending on what we chose.