Graduated Measuring Cup

thingiverse

Simple graduated cylinder - with a twist! To make it easier to label, this is a graduated cylinder within a tower. It features pouring spouts on both sides, accommodating left-handed and right-handed people alike. This project began as a math exercise: determining the heights of various cylinders for holding different volumes. Developing in milliliters is straightforward: each milliliter of volume fits into one cubic centimeter. Since one centimeter equals ten millimeters, one cubic centimeter equals 1,000 millimeters cubed. To convert to ounces, it's essential to know that one fluid ounce measures 29.574 milliliters. The formula for a cylinder's volume is base times height. The area of the base is pi multiplied by (r^2), where r represents the radius. Given the constraints of a small footprint printer (I use a Monoprice Select Mini) with maximum x, y, and z dimensions of 120 millimeters, I decided to create a cylinder with an appropriate radius so that each ten millimeter in height equals one ounce. Rearranging the equation V = pi * (r^2) to solve for r yields sqrt(V/pi) = r. Substituting Volume = 29.574 into the equation results in r = sqrt(29.574/pi). Simplifying this expression, I get r = sqrt(9.4137), which further simplifies to approximately 3.068 millimeters. Since the radius is 3.068 millimeters, the diameter of the base equals twice the radius, or 6.136 centimeters, equivalent to 61.36 millimeters.