Additional Math Pages & Resources

Thursday, August 20, 2009

Sold by weight not volume

When you see that phrase you might think of opening a new, but half-empty package of potato chips, or a box of breakfast cereal that seems mostly air. I am wondering about a box I received today from Thunderbolt Tea in Darjeeling, India.

I had ordered 7 different kinds of tea, all Darjeeling varieties. When I opened the box I was amazed to see the various sizes - what a range of packet sizes there were! Time for some math!

First we needed precision measurements, so I got my Central Tools digital caliper and a postal scale. The numbers in orange are weight (grams) and in black are dimensions (millimeters). The final number in green is a calculation of the volume of each packet.

Notice the weight only varies between 100-105 grams. That's good, because I ordered 100 grams of each variety.

(I am including the packaging because it's light, consistent between batches, and because tea can be very messy when spilled on the counter.)

The cubic volume was determined by multiplying height, width and depth in mm and then converting to liters. A liter is equal to 1,000,000 cubic mm.

The first example is 115 x 105 x 68 = 821,100 cubic mm, or .8211 liters.


Here are the 7 different
packet volumes in order of
largest to smallest:

.8211
.4224
.4200
.4150
.3542
.3494
.3240







The largest package is 2 1/2 times the volume of the smallest, for the same weight. Astonishing!









If we want a more precise comparison we can determine the relative density of the teas. Density is the amount of mass (grams) per unit of volume (liters).

We divide 1 by the volume of the tea to find out how much tea is required to fill a one liter container. Using the .4200 sample, we divide it into 1 and learn that 2.38 packages of this tea should fill a liter container.

105 g x 2.38 = 250 grams of tea per liter.

Since water is 1000 grams per liter, this tea is precisely 1/4th the density of water!

Now what I really need to know is, How do I measure to make a cup of tea?