How many cubic inches of space are inside a cube one

The number of cubic inches inside a cube is called the volume of the cube in cubic inches.

11. Make a rule for finding the volume of a cube.

12. What is the volume of a cube whose edge is 12 in.? What name is given to this amount of space?

13. A cubic foot of water weighs 62.5 lb. How much does a cubic yard of water weigh?

14. Clay soil is 2.65 times as heavy as water. What is the weight of a cubic yard of clay soil?

15. Soil rich in humus weighs about 2.5 times as much as water. What is the weight of a cubic foot of humus soil?

16. Iron weighs about 7.21 times as much as water. What is the weight of a cubic foot of iron?

17. Cork weighs about .24 times as much as water. What is the weight of a cubic foot of cork? What is the weight of a cubic inch of cork?

84. Rectangular parallelopiped. - The figure at the right represents a rectangular parallelopiped. The box in which crayon is usually supplied to schools is a familiar example of this solid.

NOTE. This solid is often called a rectangular prism in elementary schools. That name is not sufficiently accurate, mathematically; the one given in this text is preferable.

EXERCISE 109

1. After examining carefully the figure in the book, and the crayon box, make a list of the facts you observe about the edges, faces, and angles on the faces of the rectangular parallelopiped.

a. Are the edges all equal, necessarily? How many different lengths of edges do you find? How many edges are there having any one length?

b. Are the faces necessarily square? May they be square?

2. Can you find in your classroom a rectangular parallelopiped?

3. The three edges meeting at any one vertex are called the length, width, and height of the rectangular parallelopiped.

Suppose a hollow rectangular parallelopiped is 3 in. wide, 4 in. long, and 2 in. high, inside measurements.

a. How many one-inch cubes could you place in the bottom of the box?

b. How many such layers could you place in the box? c. How many cubic inches are there inside the box?

4. How many cubic inches are there inside a box if the width is 2 in., the length is 5 in., and the height is 3 in.?

5. Make a rule for finding the volume of a rectangular parallelopiped.

85. If w represents the number of linear units in the width, 7 the number of the same kind of units in the length, h the number in the height, and V the number of the corresponding cubic units in the volume, then the formula

for the volume of a rectangular parallelopiped is

V = lwh.

Remember that lwh means lxwxh.

Example. If the length is 3 ft. 6 in., the height is 2 ft.

4 in., and the width is 12 ft., find the volume.

5. 7-10 yd. 1 ft.;

h=2 yd.; and w=6 yd. 2 ft.

6. How many cubic feet of material must be moved in digging a cellar 24 ft. wide, 28 ft. long, and 6 ft. deep?

7. What is the cost of excavating the cellar in Example 6 at 75¢ per cubic yard?

8. A tank for holding water is 2 ft. high, 2 ft. 6 in. wide, and 4 ft. long.

a. How many cubic feet of water will it hold when full? b. Since there are about 7 gal. of water in one cubic foot, how many gallons of water will the tank hold?

c. If one cubic foot of water weighs 624 lb., what is the weight of the water in the tank, when the tank is full?

9. How many cubic feet of concrete are needed for a sidewalk 40 ft. long, 5 ft. wide, and 4 in. thick?

10. How many cubic yards of concrete are needed for 50 ft. of concrete road which is 16 ft. wide and averages 6 in. in thickness?

11. If a ton of soft coal occupies about 38 cu. ft., how many tons of coal will an open freight car hold, which is 36 ft. long, 8 ft. 4 in. wide, and 3 ft. high?

12. How many tons of soft coal can be stored in a coal bin 14 ft. long and 5 ft. wide, if the coal can be piled 6 ft. high?

13. A ton of timothy hay occupies about 500 cu. ft. How many tons, approximately, are there in a stack which is 30 ft. long, 15 ft. wide, and 12 ft. high?

14. A bushel of small grain (oats, wheat, etc.) occupies about 1 cu. ft. How many bushels of oats can be stored in a bin which is 10 ft. long, 8 ft. wide, and 5 ft. high?

15. A farmer needs a bin to hold about 500 bu. of oats. He can make it 9 ft. wide and 12 ft. long. How high must he make it?

16. A bushel of potatoes occupies about 1 cu. ft. a. How many bushels can be stored in a bin 20 ft. long, 6 ft. wide, and 5 ft. high?

b. How high must a bin be to hold 20 bu. if it is 2 ft. 6 in. wide and 5 ft. long?

17. A schoolroom is 25 ft. by 33 ft. by 12 ft. How many cubic feet of air are there in the room?

18. A cord of wood is 4 ft. wide, 4 ft. high, and 8 ft. long. How many cubic feet are there in a cord?

19. About how many cords of wood are there in a pile which is 8 ft. wide, 6 ft. high, and 120 ft. long?

20. Cast iron weighs about .26 lb. per cu. in.

What

is the weight of a cast iron bar which is 2 in. wide, 1 in. thick, and 5 ft. long?

21. A cubic foot of ice weighs about 58 lb. About how much does a piece weigh which is 14 in. thick, 22 in. long, and 15 in. wide?

22. How many gallons of water does it take to fill a high school swimming pool which is 20 ft. wide, 35 ft. long, and averages 5 ft. in depth? (See Example 8.)

23. A coal dealer has a bin of soft coal which is 20 ft. wide, 25 ft. long, and averages 10 ft. in height. how many tons of coal does it contain?

About

24. A road contractor has to remove soil to an average depth of 1 ft. on a street 40 ft. wide, for a distance of mile. (1 m. = 5280 ft.)

a. How many cubic yards of soil have to be removed?

b. If his teams can haul away 1 cu. yd. in each load, and if each team can haul 6 loads per day, how many days will it take 15 teams to remove the soil?

c. What will be the contractor's expense for teaming if he pays $8.50 per day for the teams?

25. Make up an example like one of the Examples 6 to 24 of this list; or, better still, measure some coal bin, grain bin, piece of ice, tank, or other object having the form of a rectangular parallelopiped, and make up the problem suggested by the object.

EXERCISE 111

Miscellaneous Review Problems

1. Find the cost of 150 barrels of salt pork at $18.757 per barrel.

2. Change to a decimal, carried out to three places.