Cube Root Word Problems

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

Monday, January 8, 1912: A regular snow storm set in this afternoon. How beautiful the snowflakes looked as they descended to ground. Am now able to extract the cube root without difficulty. Pa came for Jimmie and me this evening.

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

The teacher must have clarified how to do cube roots. Grandma was struggling with cube roots the previous Friday.

As a parent who had strong opinions during the “math wars” of the 1990’s about what should be included in (and, perhaps more importantly, what should be excluded from) the math curriculum, I’m fascinated by early 20th century math text books.

In textbooks from a hundred years ago, there is more focus on calculation than there is today but they also contain some cool word problems —Cube roots are a great example of this.

Here are some cube root word problems from a 1911 textbook called Kimball’s Commercial Arithmetic:

1. If a cubical block contains 21,952 cubic inches, how many square feet of paper will be required to cover the entire surface?

2. The entire surface of a cubic block is 384 square feet. How many 1-foot cubes can be cut from the block, allowing nothing for waste?

3. A cubical cistern holds 400 bbl. of water. How deep is it?

4. What are the dimensions of a cube that has the same volume as a box 2 ft. 8 in. long, 2 ft. 3 in. wide, and 1 ft. 4 in. deep?

The texts also contained lots of “tricks” and principles.

Principles

1. The cube of a number cannot have more than three times as many figures as its root, nor but two less.

2. If a number is separated into periods of three figures each beginning at the units’ place, the number of figures in the cube root will be the same as the number of periods.

I thought of several easy cube roots (100 is the cube root of 1.000.000. and 5 is the cube root of 125.), and decided that the principles are correct. (Of course they were correct—but somehow I felt better after I thought of a few problems to confirm it.)

If you’re a math geek, here are some previous posts that explored the math curriculum and problems from a hundred years ago.

Odd, Unusual, and Strange Math Problems

More Odd, Unusual, and Strange Math Problems

1911 Algebra Problems: The Lusitania and Molasses

Old Math Problems

An Old Mental Math Trick

Lowest Common Multiples and Highest Common Factors

Fractions in 1911 Algebra Book

5 Responses

  1. [...] test would have been on cube roots. On January 5 and January 8 Grandma wrote about struggling to learn how to do [...]

  2. Loved the coziness of this post— snow intermixed with cube roots, and topped of with “Pa coming after” them. Nice images.

    • It does have a cozy feel. And, the school would have had a wood or coal-burning stove, which (at least to me) would have added to the cozy setting.

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