CUBIC OR VOLUME MEASURE

1. Write the table of cubic measure.

A load of earth, sand, etc., is a cubic yard.

The volume of a solid is the number of cubic units it contains.

2. What is the volume of a solid 5 in. long, 4 in. wide, and 3 in. high?

The unit of measurement is 1 cubic inch. How many of these cubic units in 1 row? In 1 layer? In all the layers?

Steps taken:

First. Determine the unit of measurement.

Second. Find the number of cubic units in 1 row.

Third. Multiply the number of cubic units in 1 row by the number of rows.

Fourth. Multiply the number of cubic units in 1 layer by the number of layers.

In finding volumes the three dimensions must be expressed in the same unit of measurement (inches, feet, yards, etc.).

1. How many dimensions has a cube? How do they compare?

2. How many faces has a cube? What is their shape? How do they compare in size?

3. What is the length in feet of a 12-inch cube? The area of one of its faces in square feet? Of all its faces? Its volume in cubic feet?

4. Make and fill out a table like the following:

Continue with 48-inch, 60-inch, 72-inch, 84-inch, 96-inch, 108-inch, 120-inch, 132-inch, 144-inch cubes.

Find the volumes of these rectangular prisms:

15. What is the

by 2 in. by 2 in.?

volume of a toy building block 2 in. What is the capacity of a box that

will exactly hold 12 of them? How many can be placed

in a box 6 in. by 6 in. by 6 in.?

16. Which is larger, a 4-foot cube or 4 cubic feet? How much?

17 What 17, What is the volume of a crate that will hold 24 boxes of butter each 1 ft. long, 4 in. wide, and 4 in. high?

18. How many cubic feet in a stone step 4 ft. long, 15 in. wide, and 8 in. high?

19 A camphor chest 4 ft. long and 3 ft. wide stands 2 ft. 6 in. high. Find its volume.

20 A block of ice cream 1 ft. in. thick is served to 12 persons. of each slice?

21.XA

long, 4 in. wide, and 3 What are the dimensions

21. A man buys 14 bales of hay, each 4 ft. long, 21 ft. wide, and 2 ft. thick. How much space will they occupy n his barn? What is their value at $24 a ton, if their average weight is 150 pounds?

22. A stone pillar is 2 ft. square and 81 ft. high. What is its volume?

23. What is the capacity of a tank whose width is 3 ft., whose height is of its width, and whose length is twice its width?

24. Draw a diagram of the faces of a 4-inch cube, on a scale of 1" to 1".

25. Draw a diagram of the faces of a rectangular prism 4 ft. x 3 ft. x 2 ft. Scale 1" = 1'.

26. Find the surface area of a block of wood 3 inches square and 4 inches high.

27. How many square feet of copper will be required to line the bottom and sides of a tank 4 ft. long, 3 ft. wide, and 2 ft. deep?

28. At 6 cents a square foot, how much will it cost to line with zinc a tank 3 ft. long, 21 ft. wide, and 2 ft. deep?

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29. At 75 cents a cubic yard, what is the cost of dig. ging a cellar 24 ft. by 16 ft. by 7 ft. ?

30. How many loads of earth must be carted to fill a ditch 48 ft. long, 4 ft. deep, and of an average width of 9 ft.?

WOOD MEASURE

1. A pile of wood 1 ft. by 4 ft. by 4 ft. is a cord foot. How many cubic feet in a cord foot?

How

2. A pile of wood 8 ft. by 4 ft. by 4 ft. is a cord. many cubic feet in a cord? How many cord feet in a cord ? 3. Write the table of wood measure.

Wood, bark, etc., are generally sold by the cord.

4. How many cords of wood in a pile 20 ft. long, 4 ft. wide, and 6 ft. high?

5. A pile of wood contains 1728 cubic feet. How many cords?

6. A farmer has a wagon 12 ft. long and 4 ft. wide. How high must he pile the wood in loading a cord?

7. At $7.50 a cord, what is the value of a pile of 4-foot wood, 18 ft. long and 8 ft. high?

Find the number of cords of 4-foot wood in the following lots:

16. A railroad car 30 ft. long and 8 ft. wide is loaded.

6 ft. high with wood. What is the value of the wood at $8.75 per cord?

MASONRY

Masonry and bricklaying are usually measured by the cubic foot. In estimating the number of cubic feet in the walls of buildings, the outside dimensions are taken. This counts the corners twice, but the extra labor required to build the corners offsets their double counting.

In estimating the material required, the corners are counted once. Common bricks are 8" x 4" x 2", and, allowing for space occupied by mortar, 22 of them will lay a cubic foot.

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1. The outside dimensions of a foundation wall are 40 ft. by 28 ft. The cellar is 9 ft. deep and the walls are 2 ft. thick. Find the number of cubic feet of masonry; the number of cubic feet of material required.

40′

HINT. Reckoning the outside dimensions, the cellar walls are equivalent to a single wall 40′ + 28′ + 40′ + 28′, or 136′, in length. Reckoning exactly, the cellar walls are equivalent. to a single wall 40′ + 24′ + 40′ + 24', or 128', in length.

2. How many cubic feet of masonry in a wall 60 ft. long, 5 ft. high, and 1 ft. thick? How many bricks are required to build this wall?