Question

Problem set 2, PDF 2, Part 2 (d) - question regarding the max number of dimples of certain size. Does anybody understand how to approach this? I definitely get an answer where more than 100 dimples(r = 0.15) may exist on a sphere R=1.5. I tried many things: e.g. dividing sphere area by the dimple spherical cap area or dividing sphere area by a rectangle formed by a dimple, etc. In all cases I get an answer which says more than 100 dimples will fit on a sphere surface without overlapping. confused :-(

Answer 1

Ah, yeah it's course 18.01 as taught in 2006

Answer 2

use the rough approximation that each dimple takes pi r^2 area
then the ratio of total area of the golf ball to the total area of dimples is
\[ \frac{4 \pi R^2}{100 \pi r^2 }\]
with R/r = 10 we get
\[ \frac{4 \pi R^2}{100 \pi r^2 } = \frac{4 \pi \cdot 100}{100 \pi}= 4\]

so there is 4 times as much surface area as dimple area.

This should allow a "boundary ring"


I don't see how 100 would not fit.