5. A baseball diamond is a square which is 90 ft. on a side. Find the distance across the diamond from first base to third base.

6. A ladder 24 ft. long rests against the side of a building with its foot 6 ft. 3 in. from the building. How high on the wall of the building does the ladder reach?

7. A smoke stack 90 ft. high is to be steadied by three guy wires, which are to run from a point 10 ft. from the top of the stack to three anchors, each 40 ft. from the foot of the stack. If 3 ft. is needed for anchoring each wire, how much wire is required?

8. The rope which passes through a pulley at the top of a flagpole can be stretched out in a double strand to touch the ground at a point 30.5' from the foot of the pole. If the rope is 200' long, how high is the flagpole?

9. The accompanying figure shows the gable end of a roof. Using the dimensions given in the plan,

2'

Rafter

-48

the gable are decided upon. If the rafters are to extend 2′ 6′′ beyond the building, find the length of a rafter.

11. The figure at the right shows the dimensions for a barn.

d. The cost of a composition roof at $12.50 per square. e. The cost of painting the roof at 40¢ per square yard. f. The cost of painting the sides and ends of the barn at 50¢ per square yard if no allowance is made for windows.

12. In order to have a sufficient capacity it is necessary that a water main should have a cross-section area of 9.4 sq. ft. What is the diameter of such a pipe?

Since A = πr2, it is obvious that r2 = A ÷ π, or r = √A ÷ π.

13. What must be the diameter of an iron supporting column to give a cross-section area of 78 sq. in.?

14. A drain pipe which carries water from two branch pipes should have its cross-section area equal to the combined area of the branch pipes. If the branch pipes are 5 in. and 8 in. in diameter, what should be the diameter of the drain pipe?

METRIC SYSTEM

Metric system. This system of weights and measures originated in France about 1800. It is in general use in scientific research and in foreign trade with a large part of the world. It is therefore essential that those who are planning to enter the business world should gain a working knowledge of this system of measurement.

Metric units. The principal units of the system are the meter, the unit of length; the liter, the unit of capacity; and the gram, the unit of weight.

The meter, which is the length of one forty-millionth part of the earth's circumference passing through its poles, is equivalent

to a length of 39.37 in. The liter is the capacity of a cube which is 0.1 meter (3.937 in., or approximately 4 in.) on an edge, and the gram is the weight of a cube of distilled water which is 0.01 meter (0.3937 in., or approximately 0.4 in.) on an edge. It should be noted that the unit of capacity (the liter) and the unit of weight (the gram) are thus defined in terms of the unit of length (the meter).

In the measurement of length the relationship of the metric system to our common system is shown in the above diagram, which shows a ruler marked in centimeters (hundredths of a meter)

and millimeters (thousandths of a meter) on one edge, and in inches and sixteenths of an inch on the other.

The whole metric system is built upon a scale of 10, and hence the different measures are either decimal divisions or multiples of the principal units. These are easily learned when the significance of the prefixes which indicate the measures are learned. The fractional parts of the principal unit are indicated by the following Latin prefixes:

The multiples of the principal unit are indicated by the following Greek prefixes:

deka- which means 10

hekto- which means 100

kilo- which means 1000

myria- which means 10,000

Table of length. The meter (m.) is the unit of length, and the other measures are either decimal divisions or multiples. The following table shows those measures and their abbreviations which are in common use, and should be memorized:

1 millimeter (mm.) 0.001 meter (m.)

=

1 centimeter (cm.) = 0.01 meter

1 decimeter (dm.) =0.1 meter

1 kilometer (Km.) = 1000 meters

The meter is equivalent to a length of 39.37 in., the centimeter to 0.39 in., and the millimeter to 0.039 in. The kilometer is equivalent to 0.62 mi. The dekameter (Dm.), which is 10 m., the hektometer (Hm.), which is 100 m., and the myriameter (Mm.), which is 10,000 m., are also used.

Table of square measure. The square meter (sq. m.) is the unit in the following table:

1 square millimeter (sq. mm.)= 0.000001 square meter (sq. m.) 1 square centimeter (sq. cm.) = 0.0001 square meter

1 square decimeter (sq. dm.) = 0.01 square meter

1 sq. kilometer (sq. Km.)

= 1,000,000 square meters

The square dekameter (sq. Dm.), which is 100 sq. m., is called an are, and the square hektometer (sq. Hm.), which is 10,000 sq. m., is called a hectare, terms which are common in land measurement. A square myriameter (sq. Mm.) would be 100,000,000 sq. m.

Table of cubic measure. The cubic meter (cu. m.) is the unit in the following table:

1 cubic millimeter (cu. mm.) = 0.000000001 cubic meter (cu. m.) 1 cubic centimeter (cu. cm.) = 0.000001 cubic meter

1 cubic decimeter (cu. dm.) = 0.001 cubic meter

The table may be extended to include the cubic dekameter (cu. Dm.), which would be 1000 cu. m., the cubic hektometer (cu. Hm.), which would be 1,000,000 cu. m., the cubic kilometer (cu. Km.), which would be 1,000,000,000 cu. m., and the cubic myriameter (cu. Mm.), which would be 1,000,000,000,000 cu. m.

The cubic meter is also called a stere when used in measuring wood. Table of capacity. The liter (1.) is the unit of capacity, as shown in the following table:

1 centiliter (cl.) = 0.01 liter (1.)

1 deciliter (dl.) = 0.1 liter

1 hektoliter (H1.) = 100 liters

The liter is the same as the cubic decimeter, and is approximately equivalent to 1 qt.

There is also the milliliter (ml.), which is 0.001 1., the dekaliter (Dl.), which is 10 1., and the kiloliter (Kl.), which is 1000 1., but these measures are not commonly used.

Table of weight. The gram (g.) is the unit of weight, as shown in the following table:

1 centigram (cg.) = 0.01 gram (g.)

1 decigram (dg.) = 0.1 gram

1 kilogram (Kg.) = 1000 grams

1 quintal (Q.) = 100 kilograms

1 tonneau (T.) = 1000 kilograms

The gram is equivalent to a weight of 15.5 grains, or 0.002 lb. The kilogram, the most common measure of weight, is equivalent to 2.2 lb. The tonneau, more frequently called the metric ton, is equivalent to 2200 lb.

The other measures, the milligram (mg.), the dekagram (Dg.), the hektogram (Hg.), and the myriagram (Mg.) are not sufficiently used to be studied here.

ORAL EXERCISES

1. State the meaning of the following prefixes: centi-; kilo-; deka-; milli-; deci-; hekto-; and myria-.

2. Name the prefixes for the following: 100; 0.001; 10; 0.01; 10,000; 0.1; 1000.

3. Which prefixes are used to indicate the multiples of the principal units in the metric system?

4. In the abbreviations some begin with capital letters and others with small letters. What use can be made of this distinction in memorizing the measures?

12

Read the following:

5. 4 cm.; 18 m.; 12 Km.; 4 dm.; 45 mm.

6. 151.; 8 cl.; 29 dl.; 75 Hl.; 7 Kg.; 38 g.; 6 cg.; 5 Q.; 11 T. 7. 324 cu.m.; 114 sq. mm.; 96 cu.cm.; 45 sq. dm.; 16 cu. mm.; sq. m.; 75 sq. cm.

8. Read each expression in Exs. 5-7 as a decimal fraction or multiple of its principal unit.

Thus, 4 cm. should be read 0.04 m., and so on. Quintals and metric tons may be expressed in kilograms.

9. From the figure on page 136, state the approximate equivalents of the following: 0.1 cm.; 4 cm.; 3 cm.; 10 cm.; 6.3 cm.; 1 dm.; 1 in.; 3 in.; 1.5 in.; 21 in.; 13 in.; 33 in.

10. With a meter stick measure the length and width of your classroom; the width of your desk; the height of one of your classmates.

EXERCISES

1. The Washington monument is 555 ft. high. Express this height in meters.

2. The height of Niagara Falls is 167 ft. Express this height in meters.

3. The weight of water which passes over Niagara Falls in 1 min. is approximately 700,000 tons. Express this weight in metric tons.