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Weight of a Whale

Date: 05/24/99 at 13:19:13
From: Aaron G. Diggens
Subject: How to find the weight of a whale


My kids and I would like to know the formula to find the weight of a 
whale. A regular person like myself can't afford to buy a scale or the 
crane to lift such a beast, so how do we figure out how much it really 
weighs through mathematics? Any help you could give us would be 
greatly appreciated. Thanks.

Date: 05/24/99 at 17:45:52
From: Doctor Rick
Subject: Re: How to find the weight of a whale

Hi, Aaron.

Since a whale can float or dive, its density must be close to that of 
water. Therefore all you have to do is estimate the volume of the 
whale, and multiply the volume by the density of water. 

In the metric system, this is easy, since 1 cm^3 of water weighs 1 
gram. There are 1,000,000 cm^3 in 1 m^3, so 1 cubic meter of water 
weighs 1,000,000 grams, or 1000 kg, or 1 metric ton.

To estimate the volume of the whale, you could approximate it by a 
cylinder. Find the length and the diameter of the whale. Perhaps you 
can mathematically cut off part of the tail, since it has a smaller 
diameter than the body of the whale. In other words, imagine canning 
the whale and try to estimate the size of the can that would fit it. 
Then use the formula for the volume of a cylinder:

          2         2
  V = pi R  L = pi D  L / 4

where L is the length of the cylinder and R is the radius, or D is the

This will give you a rough estimate. If you want to be more accurate, 
the only suggestion I could make is to fill your bathtub to the brim, 
place the whale gently in the bathtub, and measure the volume of water 
that spills on the floor (and out the door and down the stairs). 

I know this could cause some difficulties, so you might choose to rent 
a tank at a local aquarium and measure how much the water level rises 
when you drop the whale in. Can you figure out how to measure the 
volume from the water-level rise?

Have fun and take good care of that whale. Remember, I only suggested 
that you MATHEMATICALLY cut off its tail or can it.

- Doctor Rick, The Math Forum   
Associated Topics:
High School Higher-Dimensional Geometry
High School Physics/Chemistry
Middle School Higher-Dimensional Geometry
Middle School Terms/Units of Measurement

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