RULE.-I. Divide the volume by the product of the terms proportional to the three dimensions, and extract the cube root of the quotient.

II. Multiply the root thus obtained by each proportional term; the products will be the corresponding sides.

2. What are the dimensions of a rectangular box whose volume is 3000 cu. ft., and its dimensions are to each other as 2, 3, and 4? 3. A pile of bricks in the form of a parallelopiped contains 30720 cu. feet, and the length, breadth, and height are to each other as 3, 4, and 5. What are the dimensions of the pile?

SIMILAR SOLIDS.

935. Similar Solids are such as have the same form, and differ from each other only in volume.

PRINCIPLES.-1. The volumes of similar solids are to each other as the cubes of their like dimensions.

1. If the volume of a cube 3 inches on each side is 27 cu. in., what is the volume of one 7 inches on each side.

OPERATION.-33: 73:: 27 cu. in. : x = 343 cu. in., volume.

2. The like dimensions of similar solids are to each other as the cube roots of their volumes.

3. If the diameter of a ball whose volume is 27 cu. in. is 3 in., what is the volume of one 7 inches on each side?

OPERATION.-/27/343 :: 3 : x = 7 in. diameter.

REVIEW OF SOLIDS.

PROBLEMS.

936. 1. What is the edge of a cube whose entire surface is 1050 sq. feet, and what is its volume?

2. What must be the inner edge of a cubical bin to hold 1250 bu. of wheat?

3. How many gallons will a cistern hold, whose depth is 7 ft., the bottom being a circle 7 feet in diameter and the top 5 feet in diameter ?

4. What is the value of a stick of timber 24 ft. long, the larger end being 15 in. square, and the less 6 in., at 28 cents a cubic foot?

5. If a cubic foot of iron were formed into a bar an inch square, without waste, what would be its length?

6. If a marble column 10 in. in diameter contains 27 cu. ft., what is the diameter of a column of equal length that contains 81 cu. ft.? 7. How many board feet in a post 11 ft. long, 9 in. square at the bottom, and 4 in. square at the top?

8. The surface of a sphere is the same as that of a cube, the edge of which is 12 in. Find the volume of each.

9. A ball 4.5 in. in diameter weighs 18 oz. Avoir.; what is the weight of another ball of the same density, that is 9 in. in diameter ? 10. In what time will a pipe supplying 6 gal. of water a minute fill a tank in the form of a hemisphere, that is 10 ft. in diameter? 11. The diameter of a cistern is 8 feet; what must be its depth to contain 75 hhd. of water?

12. How many bushels in a heap of grain in the form of a cone, whose base is 8 ft. in diameter and altitude 4 feet?

GAUGING.

937. Gauging is the process of finding the capacity or volume of casks and other vessels.

A cask is equivalent to a cylinder having the same length and a diameter equal to the mean diameter of the cask.

To find the mean diameter of a cask (nearly), Add to the head diameter, or, if the staves are but little curved, .6, of the difference between the head and bung diameters.

To find the volume of a cask in gallons,

Multiply the square of the mean diameter by the length (both in inches) and this product by .0034.

1. How many gallons in a cask whose head diameter is 24 inches, bung diameter 30 in., and its length 34 inches?

2. What is the volume of a cask whose length is 40 inches, the diameters 21 and 30 in., respectively.

3. How many gallons in a cask of slight curvature, 3 ft. 6 in. long, the head diameter being 26 in., the bung diameter 31 in. ?

'Of volume × 1.2407.

Of surface x 1.77255.
'Of volume × 3.8978.

Of surface x 2821.
3 Of volume x .6204.
Radius x 1.1547.

6. The Side of Inscribed Cube Diameter x .5774.

METRIC SYSTEM

The edges of this cube are each 1 Me'ter, or 10 Dec'i-me'ters, or 100 Cen'time'ters, in length.

941. The Metric System of weights and measures is based upon the decimal notation, and is so called because its primary unit is the Me'ter.

942. The Me'ter (m.) is the base of the system, and is the one ten-millionth part of the distance on the earth's surface from the equator to either pole, or 39.37079 inches.

Me'ter means measure; and the three principal units are units of length, capacity or volume, and weight.