First, we used an approximation to estimate the height (~25.9cm) and radius (~3.8cm) of a Pringles can to model a cylinder in Mathamatica. We used these approximations to calculate the volume of the cylinder (Volume = πr2h) and we found the volume to be 1174.94cm3. Next, we approximated the shape of a pringles chip with the formula for a saddle (f(x,y) = 17 + x2 – y2). We used 17 cm as the z-intercept in order to fit the approximation of the saddle shape into the cylinder. We also estimated that the height of each Pringles chip to be about 3 cm tall.
Using an iterated integral, we approximated the volume under the saddle shape to estimate the volume of the pringles in the can, which is about 346.5 cm3. Then, we used Mathematica to visualize the volume of the pringles in the can. Then we combined both graphs to display our approximated figures. This shows that our approximations of the chip fits within our approximation of the can.
