Ray's New Higher Arithmetic · Arts. 199–204 · Unit 11: Compound Denominate Numbers

50. Solids, capacity and angles

Goal: Your student uses cubic measure, the cord, liquid and dry measure, and the table of angular measure.

⏱ About 40 minutes · 7 steps

Open it at the Internet Archive ↗

You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Solid or cubic measure (cubic inches, feet, yards; the cord of wood and perch of stone), measures of capacity (liquid measure, apothecaries' fluid measure, dry measure with the Winchester bushel), a comparison of the gallon and bushel in cubic inches, and angular or circular measure (seconds, minutes, degrees).

The lesson, step by step

  1. Warm-up

    Ask: How many small cubes 1 inch on a side fit in a box 12 inches each way? (1728.)

  2. Solids

    Read:

    A Solid has length, breadth, and thickness.

    A Cube is a solid, bounded by six equal squares, called faces.

    Table: 1728 cu. in. = 1 cu. ft., 27 cu. ft. = 1 cu. yd. A cord of firewood is 128 cubic feet (a pile 8 ft. long, 4 ft. wide, 4 ft. high).

  3. Capacity

    Read:

    Capacity means room for things.

    Liquid measure: 4 gills = 1 pint, 2 pt. = 1 quart, 4 qt. = 1 gallon, and a gallon holds 231 cubic inches.

    Dry Measure is used for measuring grain, fruit, vegetables, coal, salt, etc.

    2 pt. = 1 qt., 8 qt. = 1 peck, 4 pk. = 1 bushel.

  4. Medicine

    Read:

    Apothecaries' Fluid Measure is used for measuring all liquids that enter into the composition of medical prescriptions.

    60 minims = 1 fluid drachm, 8 fluid drachms = 1 fluid ounce. Just look; no need to learn it.

  5. Angles

    Read:

    A plane angle is the difference of direction of two straight lines which meet at a point.

    Every circumference contains 360 degrees.

    Table: 60" = 1', 60' = 1°, 360° = 1 circumference. A right angle is 90°.

  6. Practice

    Your student finds: cubic feet in a wood pile 16 ft. long, 4 ft. wide, 4 ft. high, and how many cords that is; pints in 3 bushels; minutes in a right angle.

  7. Wrap-up

    Ask: Is a liquid quart the same as a dry quart? (No; the book's comparison table shows the dry quart is larger.)

Answers to the book's problems

Practice: 16 × 4 × 4 = 256 cu. ft. = 2 cords; 3 bu. = 192 pints; a right angle = 5400 minutes.

Worked out for this site from the scan. If a number in your copy differs, trust the book.

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