__
The Great
Bucket Lesson__

(TC, & Fizzle, 2007)

I am a
walrus and this is my bucket. Don’t
even think of taking this bucket, because it’s mine and not yours.
I know it’s my bucket because I measured it.
I know its height, its volume, its area and its weight.
If you don’t believe me, I will show you how.

First, I
measured my bucket’s height with a ruler.
My ruler is twelve inches, which is one foot long.
I measured in inches. An
inch is a measurement of length. We
are measuring the height, which is the length of the top to the bottom of my
bucket. Inches are a measure of length from the United States customary system,
which is adapted from the British imperial system.
Here is a chart of the relationship of length:

1 foot (ft)
12 inches (in)

1 yard (yd)
3 feet (ft)

1 mile (mi)
1760 yards (yd)

My ruler is
divided into sixteenths of an inch.
That means that each inch is broken into sixteen equal parts.
Therefore, you can measure to the nearest sixteenth. If you measure and
object and the resulting measurement falls between two lines, you measure to the
line that the object is closer to.
So if a measurement falls between 1/8 and 1/4 of an inch, and is closer to the
1/4 line; that measurement would be 1/4 inch.
If you were to measure something, it fell between 1/2 and 5/8 of an inch,
and it was closer to the 1/2 line; you
would measure it as 1/2 inch. Even
if it appeared like the measurement was exactly, center between the lines on the
ruler, we would still have to use an approximation or estimate for it.
That is because the ruler does not measure to anything higher than
sixteenths. Halfway between two sixteenth measurements would be thirty-seconds,
and we cannot be sure of the accuracy of that measurement.
We have to work within the limitations of our measuring instrument, which
is sixteenths. If the measurement
falls on the dead center between lines, round up to closest measurement.

We prefer
approximations, because they use careful measurement and mathematic principles
to round to the nearest value. With
approximations we do all the calculations as accurately as possible to get the
best, closest answer we can get with the measuring instruments at our disposal.

On the other
hand, estimates are quick assessments that we do in our heads to get an answer
that will work in a pinch. It is
not necessarily accurate or correct, but an estimate can give us an idea about
the measurement of something. For
example, looking at a bucket of fish, we can do a quick visual count and say,
“There are about fifteen fish in there.”
To estimate, we would be certain to count every fish and every part of
the fish in the bucket. We would
then say something like “There are approximately fourteen and a half fish in my
bucket.” Walruses prefer to approximate
when they can. We are not very good
at doing things in our heads, so we take our time on paper or with a calculator.
We also like to be certain exactly how many fish we have in our buckets.

(Bertau, date unknown)

I like to
convert my measurements to decimal points.
I find it makes it easier to do the calculations.
Like most other walruses, I like to do things the easiest way I can.
You can see in the picture below, that the height of my bucket is
approximately 2 7/16 inches or 2.4375 inches.

But that
doesn’t tell me how many fish my bucket can hold.
I need to calculate the volume to see how much it holds.
I know that a bucket is a frustum.
A frustum is a cone with its tip cut off.
The formula for determining the volume of a frustum is:

Volume = ((pi * h) / 3) * (R^{2} + Rr +r^{2})

Where:

·
h = Height

·
R = Bottom (Big) Radius

·
r = Top (Small) Radius

Radius is half of the diameter, which is the measurement across a circle,
through the center point of the circle and ending on points on either side of
the center point. I measured the
diameter of my bucket. I used my
ruler to measure the length between each edge of my bucket, through the middle
point.

On the large
end of my bucket, the diameter was about 2 1/4 inches or 2.25 inches.
That gives me a radius of 1 1/8 inches or 1.125 inches.

On the small end of my bucket, again I used my ruler to measure the length
between each edge of my bucket, through the middle point.
I measured a 1 1/2 diameter or 1.5 inches.
The diameter divided by two would be 3/4 of an inch or .75 inches.

The formula for volume is ((∏
* h) / 3) * (R^{2} + Rr +r^{2}).
Oh yeah,
∏
also known as
Pi is approximately
3.14159265. People have not been
able to calculate Pi to its last digit because it’s an
irrational number. It
cannot be written as a fraction (the ratio of two integers).
The only Pi most walruses worry about is fish pie in their buckets, but
they are always losing their buckets.
Since my bucket is so important to me, I learned about Pi.
So, if
I plug all my measurements into the formula Volume = ((∏
* h) / 3) * (R^{2} + Rr +r^{2}).
It looks like this.

Volume = (( 3.14159265 *
2.4375)/3) *
(1.125² + 1.125 * .75 + .75²)

Volume =
(2.552544028125) * (1.265625 + 0.84375 + 0.5625)

Volume =
2.552544028125 * 2.671875

Volume =
6.820078575146484 cubic inches

The volume
of my bucket is about 6.8201 cubic inches.

To calculate the area of my bucket, I needed to use the same measurements I
already measure to calculate the volume; and put them into the formula to
calculate the area of a frustum. It
is:

Area = ∏ (R + r) √(R – r)² + h²

Area =
3.14159265 (1.125
+ .75)
√(1.125 - .75)² + 2.4375²

Area =
3.14159265 (1.875)
√(0.375)² + 5.94140625

Area =
5.89048621875
√0.140625 + 5.94140625

Area =
5.89048621875
√6.08203125

Area =
5.89048621875
* 2.4661774571186072699929663487117

Area =
14.526984324149075208087128686519 square inches

But my
bucket doesn’t have any area on the opening.
So we need to subtract that part from the total area.
To do that, we need to use the formula to calculate the area of a circle.
That is:

A=∏r²

So the area (A) of the top of my bucket would be:

Area =
3.14159265 (1.125²)

Area =
3.14159265
(1.265625)

Area =
3.97607819765625 square inches

So if we
subtract 3.97607819765625 from 14.526984324149075208087128686519, we get
10.550906126492825208087128686519 square inches.

So the area
of my bucket is approximately 10.5509 square inches.

The weight
of my bucket was easy to measure.
Weight is a measurement of how heavy an item is.
Weight measure the mass an object here on the planet Earth, on other
planets my bucket would have a different weight.
But we are measuring my bucket on Earth, so we are not going to worry
about other planets for now.

My scale
could measure in ounces or grams. I
chose to measure in grams. A gram
is or g is a metric unit of measure.
That means that all the measurements are in a scale of ten. Here is a
list of the common units of weight in the metric system:

1 metric ton
= 1,000 kilograms

1 kilogram
(kg) = 1,000 grams

1 gram (g) =
1,000 milligrams

1 milligram
(mg) = 1,000 micrograms

First, I
made sure my scale was on and zeroed out.

Next, I put
my bucket on the scale and carefully read the result.
Since my scale is digital, it does the approximation for me.
It measures to the tenths place.

My bucket
weighs approximately 21.8 grams or 21.8g.
That would be the same as 21800mg or 0.0218kg.

(Unknown, 2007)

You may say
that a bucket that is 2.4375 inches high, with a volume of 6.8201 cubic inches,
an area of 10.5509 square inches and a weight of 21.8 grams is kind of small for
such a large walrus as me. However,
I can tell you with certainty that it is not.
Even though I am large and weigh about 1,700 kilograms, my bucket is just
fine. It is very portable and fits
nicely in my pocket when I wear pants. I just need to fill it up frequently.

__
References:__

TC, & Fizzle, J. (Photographer). (2007). *Walrus*.
[Web]. Retrieved from

http://stillfootball.wordpress.com/2007/06/30/the-straw-that-stirs-

the-drink-and-other-cliches/

Bertau, P. (Photographer). (date unknown). *Buckets of trout, mangrove*

*
snapper, ribbon fish and a blue eyed sea robin!*.
[Web]. Retrieved

from http://www.bertaut.com/snapper.html

Unknown. (Photographer). (2007). *I
am the lolrus*.
[Web]. Retrieved from

http://cheezburger.com/View/2666929920

Translation
of Pacific Walrus dialect to American English done by Margret Treiber.