Huge congratulations to Barbara
Fontana who guessed the exact number of jellybeans in the jar -
Bryony Dyer and Barnaby Gregory were very close behind though,
both guessing 737! Thanks to all who got involved, we love doing
these little competitions and the hundreds of e-mail responses we
receive just make us laugh! We thought we would share the most
impressive response we got with you. This is from Bailey F, who
was only off-bean by 9!
"As a scientist, I'm going to need to
work through this in a logical way showing all my working. My
answer's at the bottom.
First of all, I'm immediately going to
take 1cm off the circumference to account for the thickness of the
glass (the inner circmference will always be a bit less than the
outer circumference. I'll also take a bit off the height to account
for the lid, the thickness of the glass at the bottom of the jar,
and the bit of empty space at the top. Let's go with 16cm.
So new assumptions: 35cm
circumference, 16cm height
Volume of a cylinder = pi(r^2) * h
r = (35/pi)/2 = 5.57
so, volume of jar = pi * 5.57 * 5.57 *
16 = 1558 cm^3
Now we need to figure out the volume
of a jelly bean. As a rough measurement, I'll say it's a cylinder
with radius 0.5 cm and length 2 cm.
So, volume of jelly bean = pi * 0.5
*0.5 * 2 = 1.57 cm^3
The maximum number of jelly beans that
the jar could fit would therefore be 1558/1.57 = 992
However, there will be a certain
amount of empty space between the jelly beans that needs to be
accounted for. I'd take off another 20% but I also haven't
accounted for the tapering at the top of the jar so let's go for
25%. 0.75 * 992 = 744
Therefore there are 744 jelly
beans in the jar."