Imagine a cylindrically shaped object with diameter D and height (length) h. a)
ID: 1523022 • Letter: I
Question
Imagine a cylindrically shaped object with diameter D and height (length) h. a) h/D = 0.7 for the given values. Someone makes a scale model of the object that is either larger or smaller than the actual cylinder. If the scale model is to look like the actual cylinder how must the quantities h and D be related for the scale model? Explain your reasoning^2. b) Describe how h and D would have to be related if the cylinder changed size and the reseated cylinder was distorted so that it was narrower and stretched vertically compared to the original? Repeat for a rescaled cylinder that was distorted so that it was wider and squished vertically. Explain your reasoning in each case. Don't make up values for D and h. There are an infinite number of possibilities in each case, but these questions have definite answers. c) Sketch on the same set of axes (no need for graph paper) three linear functions: one describing how h is related to D for rescaled cylinders that are not distorted, a second describing the stretched vertically cylinders, and a third describing the squished cylinders. Describe the slope and intercept of each line.Explanation / Answer
As, Volume of cylindrical object , V = pi * D2 * h/4
Thus, relation between h and D
=> pi * D2 * h/4 = 1
=> D = 2 * sqrt[1/(pi * h)]