Capacity (Volume) Word Problems

17-year-old Helena Muffly wrote exactly 100 years ago today: 

Thursday, January 16, 1913:  We had an examination in Geometry this morning. I think I will make a better mark than what I did the other time.

Source: Kimball's Commercial Arithmetic (1911)

Source: Kimball’s Commercial Arithmetic (1911)

Her middle-aged granddaughter’s comments 100 years later:

What was the Geometry test about—proofs? . . . angles? . . . shapes? . . . capacities?

The directions for doing capacity problems in a hundred-year-old textbook (I think it was called volume by the time I was in school. Is capacity the same thing as volume?) seem very different from what I remember doing when I was a student:

The method of finding the contents of any regular vessel in gallons, bushels, barrels, etc. is called gauging.

The capacity of tanks, cisterns, etc. is usually expressed in gallons or barrels. In every liquid gallon there are 231 cu. in.

To find the exact number of gallons in any vessel, divide the number of cubic inches in the vessel by 231.

To find the number of gallons in a cylindrical vessel, multiply the square of the diameter by the height, and this product by 5 7/8.

To find the approximate number of gallons in a cistern, multiply the number of cubic feet by 7 1/2 and from the product, subtract 1/400 of the product.

The capacity of bins, etc. is usually expressed in bushels. The standard bushel in the United States is a measure 8 inches deep, 18 1/2 inches in diameter, and contains 2150.42 cubic inches.  Hence, to find the number of bushels in any bin, divide the number of cubic inches in the bin by 2140.42.

Kimball’s Commercial Arithmetic (1911)

Got that?  Want to try some problems?

  1. Find the contents in gallons of a tank 4 ft. square and 5 ft. deep.

  2. The water in a cistern 8 ft. square is 2 ft. deep, how many gallons does it contain?

  3. A bin 8 ft. by 4 ft. by (?) contains 90 bushels of grain. Find the missing dimension.

  4. How many tons of water will fill a tank 11 ft. 8 in. by 3 ft. 6 in. by 2 ft. 3 in., if the weight of a cubic foot of water is 1,000 ounces?

11 Responses

  1. At least the problems seem to have some real world applications! :)

  2. too hard, brain won’t work, I have no neighbours paper to look at

  3. I calculated the first two in my head, and then it got too complicated. Glad that we have calculators today and not slates :-).

  4. that is way to hard for me, I would fail badly! x

  5. Finally in today’s schools we’ve come full circle. Sixth grade math is now teaching what they are calling ‘word skills’ and it looks a lot like the question posted above with a different equation for it to fit modern life.

  6. Put numbers in from of me and my brain turns to slush… a childhood condition which has chosen to remain :-D

  7. ooops… *front*

  8. I agree way to hard for me too, I admire them back then for the hard work on their class work, I have gotten too soft on my computer. I am glad to read from Sheri that some of that type of work is making its way back to the class room – too many young adults I come into contact have no word skills, are unable to comprehend or reason out problems. I used to ask why do we need all that “stuff” that has nothing to do with life, as I got older I realized why we needed it and wished I had paid better attention in school.

  9. what grade was Helena in? I printed these problems out for my boys to do. :)

    • She went to an old-fashioned 3-year high school. She was in her final year of high school. I guess that she’d be called a senior, but I’m not sure.

      I hope your boys enjoyed the problems. :)

  10. Oh Gosh, not thanks! I don’t even want to attempt. My 13 year old brings home her math and she is on her own! Thank goodness for the library tutors and google! ;-)

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