How long would it have to rain to fill half a coconut?

Answer 1

This is a funny question!

If the coconut is still on the tree, the rain will never fill half of it!
If the coconut is not on the tree, but hasn't been opened yet, who knows when it might even begin to be filled!

If it has been opened, and all the contents have been eaten, and the shell is neatly in two halves, but if the open sides of the shells are facing the ground, neither half will fill with rain!

BUT, if all is going to plan, and you have at least one half of an empty coconut shell, and it has no holes in it, and the open side is to the sky, AND IT IS RAINING, you will still not be able to calculate how long it will take to fill half a coconut! because ...

1. you don't know how much rain is falling per minute in a given area.

Also, on the basis of the information in the question:
2. you don't know the size/capacity of the coconut shell!

HOWEVER! If the coconut is spherical and has an internal (empty space) diameter of, say, 6 inches:-

1. The disk-shaped area of the top of half the coconut is π r2 (r is the radius of the circle, π is Pi, approximately 3.14159)
is 3.14159 x 3 x 3, i.e. 28.27433388 sq ins.

2. So, at 1 inch per minute, 28.27433388 cubic inches of rain will fall into the coconut per minute.

3. The volume/capacity of a half a sphere is 2/3 π r3, so the capacity of the coconut is: 2/3 x 3.14159 x 3 x 3 x 3, which is 56.5486676 cubic inches.

4. So capacity divided by inflow is exactly 2 (minutes)

NOTE: This final calculation, at step 4, has been done using a more accurate figure for Pi, not the approximations shown for illustration purposes in the earlier steps of the calculation.

QUICK TIPS:

1. The time in minutes, if the rainfall is 1 inch per minute, is always 1/3rd of the diameter in inches. (Because there is always the same ratio of flat open disk area to volume, regardless of size)
So, for example, a 6 inch diameter shell will half-fill in 2 minutes (6 divided by 3). See above for 'full' calculations.
A 9 inch diam shell will take 3 mins
and a 300 inch diameter shell will half-fill in... um ... 100 mins. Easy!
And a 4 inch diam shell will half-fill in 1.3333 minutes, which is 1 minute and 20 seconds. You could almost do even this one in your head!

2. If the amount of rainfall doubles, e.g. to 2 inches per minute, the half shell will filll twice as quick, i.e. in half the time! So rainfall at 2 ins per min will half-fill a 6 inch diam shell in (6 divided by 3, divided by 2) one minute!

FORMULA: Half a coconut shell will always fill in this number of minutes:

d/rpm/3

i.e. d divided by rpm, then answer divided by 3,
where d = diameter (in whatever unit of measure), and
rpm = rate of rainfall per minute in the same unit of measure as d.

• For more information about calculating the size of a disk (the area of a circle) and the volume/capacity of a sphere, see Related links below.