Oblique Sculpture
Your team of architects has been commissioned by the city of Chicago to design a new building for downtown. Together your team decides to design a building that is shaped as an oblique pyramid that is covered with glass. The City Council wants a scale model of the building.
Your task is to design and produce a scale model of the oblique pyramid and determine the amount of glass needed.
Include all necessary measurements on your 3-D design. What is your scale?
Ice Cream Wrapper
You have been hired by the owner of a local ice cream parlor to assist in his company’s new venture. The company will soon sell its ice cream cones in the freezer section of local grocery stores. The manufacturing process requires that the ice cream cone be wrapped in a cone-shaped paper wrapper with a flat circular disc covering the top. The company wants to minimize the amount of paper that is wasted in the process of wrapping the cones. Use a real ice cream cone or the dimensions of a real ice cream cone to complete the following tasks.
Sketch a wrapper like the one described above, using the actual size of your cone. Ignore any overlap required for assembly.
Use your sketch to help you develop an equation the owner can use to calculate the surface area of a wrapper (including the lid) for another cone given its base had a radius of length, r, and a slant height, \(\ell\).
Using measurements of the radius of the base and slant height of your cone, and your equation from the previous step, find the surface area of your cone.
The company has a large rectangular piece of paper that measures \(100\) cm by \(150\) cm. Estimate the maximum number of complete wrappers sized to fit your cone that could be cut from this one piece of paper. Explain your estimate.
Your team of architects has been commissioned by the city of Chicago to design a new building for downtown. Together your team decides to design a building that is shaped as an oblique pyramid that is covered with glass. The City Council wants a scale model of the building.
Your task is to design and produce a scale model of the oblique pyramid and determine the amount of glass needed.
Include all necessary measurements on your 3-D design. What is your scale?
Ice Cream Wrapper
You have been hired by the owner of a local ice cream parlor to assist in his company’s new venture. The company will soon sell its ice cream cones in the freezer section of local grocery stores. The manufacturing process requires that the ice cream cone be wrapped in a cone-shaped paper wrapper with a flat circular disc covering the top. The company wants to minimize the amount of paper that is wasted in the process of wrapping the cones. Use a real ice cream cone or the dimensions of a real ice cream cone to complete the following tasks.
Sketch a wrapper like the one described above, using the actual size of your cone. Ignore any overlap required for assembly.
Use your sketch to help you develop an equation the owner can use to calculate the surface area of a wrapper (including the lid) for another cone given its base had a radius of length, r, and a slant height, \(\ell\).
Using measurements of the radius of the base and slant height of your cone, and your equation from the previous step, find the surface area of your cone.
The company has a large rectangular piece of paper that measures \(100\) cm by \(150\) cm. Estimate the maximum number of complete wrappers sized to fit your cone that could be cut from this one piece of paper. Explain your estimate.