Volume by 64 French Fries

thingiverse

We approximate the volume below the surface z=16-x^2-2y^2 and above the square [0,2]x[0,2] with a double Riemann sum. We take the [0,2]x[0,2] square and divide it into 64 smaller squares by subdividing it. Then we create a rectangular prism by choosing the height to be the function value in the center of each square. The height is also reduced by scaling down by a factor of four. The resulting collection resembles a stack of skinny fries! Together with Volume by 16 and No Skinny Fries, this shows how a double Riemann sum can approximate a volume. (See https://www.thingiverse.com/thing:917032 and http://www.thingiverse.com/thing:918151.) This model was created and printed by my WLU summer research student Ryan McDonnell ('17).