The Great Bucket Lesson
(TC, & Fizzle, 2007)
I am a walrus and this is my bucket. Donít even think of taking this bucket, because itís mine and not yours. I know itís my bucket because I measured it. I know its height, its volume, its area and its weight. If you donít believe me, I will show you how.
First, I measured my bucketís 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, ďThere are about fifteen fish in there.Ē 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 ďThere are approximately fourteen and a half fish in my bucket.Ē 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 doesnít 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) * (R2 + Rr +r2)
∑ 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) * (R2 + Rr +r2). Oh yeah, ∏ also known as Pi is approximately 3.14159265. People have not been able to calculate Pi to its last digit because itís 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) * (R2 + Rr +r2). It looks like this.
Volume = (( 3.14159265 * 2.4375)/3) * (1.125≤ + 1.125 * .75 + .75≤)
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 Ė r)≤ + h≤
Area = 3.14159265 (1.125 + .75) √(1.125 - .75)≤ + 2.4375≤
Area = 3.14159265 (1.875) √(0.375)≤ + 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 doesnít 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:
So the area (A) of the top of my bucket would be:
Area = 3.14159265 (1.125≤)
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.
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.
TC, & Fizzle, J. (Photographer). (2007). Walrus. [Web]. Retrieved from
Bertau, P. (Photographer). (date unknown). Buckets of trout, mangrove
snapper, ribbon fish and a blue eyed sea robin!. [Web]. Retrieved
Unknown. (Photographer). (2007). I am the lolrus. [Web]. Retrieved from
Translation of Pacific Walrus dialect to American English done by Margret Treiber.