MEASURE OF VOLUME

153. Volume or solid contents has three dimensions: length, breadth, and thickness. The unit of measure for volumes is a cube.

TABLE FOR CUBIC MEASURE

1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.)

27 cubic feet

= 1 cubic yard (cu. yd.)

Note. In measuring wood, 128 cu. ft. is sometimes called a cord, but more often a pile 8 ft. long and 4 ft. high is called a cord, and the length of the wood named. A cord of 4-ft. wood contains 128 cu. ft., but a cord of 2-ft. wood is often estimated as described and contains, if thus estimated, only 64 cu. ft.

A cord of 18-in. wood contains, if estimated by the pile of 8 ft. in length and 4 ft. in height, only 48 cu. ft. Custom varies in different sections of the country about the measurement of wood.

154. In measuring the contents of bins in bushels, 2150.42 cubic inches for a bushel are used.

In estimating the contents of bins in bushels, 1.25 cubic feet to the bushel is sufficiently accurate.

155. In measuring the contents of tanks in gallons, 231 cubic inches to the gallon are used.

In estimates 7.5 gal. to the cubic foot is sufficiently accurate.

156. Finding the Cubic Contents or Volume of Rectangular Solids

157. The volume of a rectangular solid is found by applying the unit of measure to each of its three dimensions and finding the product of the results.

In the figure shown above the unit of measure may be applied to the width 2 times, to the height 2 times, and to the length 4 times. The solid, therefore, contains the unit of measure 2 × 2 × 4 or 16 times.

If the dimensions of the solid were given in inches, the unit of measure would be a cubic inch, and the volume of the solid 16 cubic inches. If the dimensions were given in feet or yards, the unit of measure and the volume would be named in corresponding terms of cubic measure.

Applications of Cubic Measures

158. 1. How many cubic feet in a rectangular stone wall, which is 2 ft. thick, 5 ft. high, and 16 ft. long?

2 cu. ft. × 5 × 16

cu. ft. Ans.

2. How many cubic yards of earth will be removed in digging a cellar 24 ft. wide, 40 ft. long, and 6 ft. deep?

24 cu. ft. x 40 × 6=5760 cu. ft.

3. How many cubic yards of earth will be needed to raise the surface of a lawn 6 in., if the lawn is 30 ft. wide and 36 ft. long?

540 cu. ft. (54027) cu. yd. = 20 cu. yd.

=

4. How many cubic feet of water will a tank hold which is 18 in. deep, 4 ft. wide, and 10 ft. long?

5. How many stricken bushels of grain will a bin hold whose inside dimensions are 4 ft. by 3 ft. by 8 ft.?

6. How many bushels of apples will such a bin

hold?

7. What is the volume in cubic yards of a rectangular block of stone 18 in. by 24 in. and 9 ft. long?

8. My sleeping room is 10 ft. long, 9 ft. high, and 8 ft. wide. How many cubic feet of air does it contain?

9. How many gallons of water will a tank contain that is 4 ft. long, 3 ft. wide, and 18 in. deep?

10. A coal bin is 22 ft. long, 12 ft. wide, and 6 ft. deep. How many tons of coal will it hold, allowing 35 cu. ft. to the ton?

11. In a tank which is 4 ft. wide and 6 ft. long the water is 9 in. deep. How many gallons of water in the tank?

12. A wagon box is 2 ft. 9 in. wide and 10 ft. long. How high must the sides be to hold 1 cu. yd. of earth?

13. A stone wall is 2 ft. thick at the bottom and 1 ft. thick at the top. It is 5 ft. high and 100 ft. long. How many cubic yards of stone does it contain? (Use the average thickness in the computation.)

14. How many bricks, allowing 22 to the cubic foot, will be required to build a brick wall 16 in. thick, 4 ft. high, and 18 ft. long?

15. How high will a bin which is 7 ft. wide and 8 ft. long have to be to hold 10 T. of coal? (Estimate volume of each ton of coal as 35 cu. ft.)

16. How much water will a cistern hold which is 4 ft. square and 5 ft. deep?

17. How much water will a cistern hold which is cylindrical and 4 ft. in diameter and 5 ft. deep?

(The volume of a cylinder is .7854 of the volum of a square prism of like dimensions.)

4 x 4 x .7854 x 5, the number of cubic feet.

18. How much water will a cylindrical boiler, such as is used in kitchens, hold if it is 12 in. in diameter and 5 ft. in length?

19. How many gallons of water will a circular tank hold which is 10 ft. in diameter and has perpendicular sides 2 ft. in height?

20. A silo is often made cylindrical in shape. How many cubic feet of space in such a silo which is 20 ft. in diameter and 15 ft. in height?

21. The water in a well which is cylindrical in shape and 3 ft. in diameter is 10 ft. deep. How many barrels of water in the well?

22. How much earth must be removed in digging a well 5 ft. in diameter and 20 ft. in depth, if it is cylindrical in shape?

23. Cast iron weighs about 450 lb. to the cubic foot. What is the weight of a rectangular piece of cast iron 3 in. thick, 4 ft. wide, and 6 ft. long?

24. What is the weight of a cylindrical bar of steel 2 in. in diameter and 6 ft. long? (Steel weighs about 490 lb. to the cubic foot.)

25. What is the weight of a rectangular piece of wrought iron 2 inches square and 6 feet long? (Wrought iron weighs about 480 pounds to the cubic foot.)