Finding the degree to cover a flare shape

Question

I have a lamp shade frame that I want to cover with bamboo slats. The top is 12" around and the bottom is 33" around. The distance from the top to the bottom most part is 6". What degree, with minor variation due to unequal slat width, would I need to have from top to bottom to have the pieces line up edge to edge? Most pieces average ⅝" wide.

Answer 1

Along the wider bottom ring, you can line up $33/(\frac58)=52.8$ slats.

Assuming you will trim the slats into wedges which are $\frac58''$ at the bottom and smaller at the top (to fit the smaller upper ring), those 52.8 slats will need to each have a top width of $12/52.8\approx 0.227''$.

Assuming that the slant height is $6''$, the angle at the bottom corner of each slat would be $\arctan\frac{6}{(5/8-12/52.8)/2}\approx 88.102^\circ$.

Hope I didn't make an error here. The last slat may have to be custom trimmed.