Volume by 16 French Fries

thingiverse

We estimate the volume beneath z=16-x^2-2y^2 and above the square [0,2]x[0,2] using a double Riemann sum. We divide the [0,2]x[0,2] square into 16 smaller squares, then create a rectangular prism by selecting the height to be the function value at the center of each square. The height is also reduced by a factor of four. The resulting collection resembles a stack of sticks! \n\nCoupled with Volume by 64 & no Sticks, this illustrates how a double Riemann sum can approximate a volume. (View https://www.thingiverse.com/thing:917118 and http://www.thingiverse.com/thing:918151.) \n\nThis model was developed and printed by my WLU summer research student Ryan McDonnell ('17).