Ray's New Practical Arithmetic · Art. 70 · Unit 7: Reduction of Compound Numbers
37. Cubic measure
Goal: Your child finds the volume of a box shape by multiplying length, breadth and height, and uses cubic feet, cubic yards and cords.
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: the cube, why a cubic foot holds 1728 cubic inches, the table (cubic inches, feet, yards, the cord of wood), and 11 problems on boxes, cellars and woodpiles. Answers are printed.
The lesson, step by step
Warm-up
Mental: 3 × 3 × 3? 2 × 2 × 2? 12 × 12?
What a cube is
Read:
Solid or Cubic Measure is used in measuring things having length, breadth, and thickness.
A Cube is a solid, having 6 equal faces, which are squares.
Build a 2 × 2 × 2 cube from sugar cubes or blocks and count: 8.
Why 1728
A cubic foot is 12 inches long, 12 wide and 12 high. 12 × 12 = 144 in one layer, and 12 layers: 144 × 12 = 1728 cubic inches. In the same way a cubic yard is 3 × 3 × 3 = 27 cubic feet.
The cord
Table: 128 cubic feet (a pile 8 ft. long, 4 ft. wide, 4 ft. high) make 1 cord. Note for you: firewood is still sold by the cord.
Guided practice
Together:
How many cubic feet in a rectangular solid, 8 ft. long, 5 ft. wide, 4 ft. thick?
In a pile of wood 40 feet long, 12 feet wide, and 8 feet high, how many cords?
(160 cu. ft.; 3840 ÷ 128 = 30 cords.)
Independent practice
Your child does problems 1 to 5 and 7 to 11.
Check and wrap-up
Answers are printed. Measure a real box and find how many cubic inches it holds.