133. In a board 4m long and 0.4m wide, how many square decimeters?

134. If a stone 1.25m long, 0.72m wide, and 0.4m thick, weighs 1 ton, what is its specific gravity?

135. Find the cost of 75.6 meters of velvet at $2.50 a meter. 136. Find the weight of 31.5 hektoliters of grain at 45 grams a liter.

137. How many kilos of pure water will it take to fill a rectangular cistern 2 meters deep, 1.5 by 1.75 meters in its other two dimensions?

138. How many kilos do 115 hektoliters of water weigh? Of milk?

139. At $0.17 a dekaliter what must be paid for 25.3l of

corn?

140. What is the capacity of a jar that weighs when empty 275, and when filled with water weighs 8.25k?

141. What is the weight in grams of 253.2cucm of milk?

142. If I buy 25 liters of alcohol, and it weighs 22 kilos, is it pure?

143. How many cubic decimeters in a mass of cast-iron that weighs 108 tons?

144. What will a rectangular prism of copper whose dimensions are 8 by 5 by 3cm weigh?

145. If a cistern is 2.5m long, 15 dm wide, and 75 cm deep, how many liters will it hold? How many metric tons of water?

146. Brass contains 4 parts of copper to 3 of zinc. How much of each metal is there in 1723.4 grams of brass?

147. What is the weight of a bar of iron 5 meters long, and 3 by 4 centimeters in the other two dimensions?

148. How many liters in 327 kilograms of pure milk?

(For Metric Equivalents see Appendix, p. 374.)

COMPOUND NUMBERS.

229. A Simple Number consists of but one kind or denomination; as 2, $4, 8 books, 5 men, 6 days, 10 miles.

230. A Compound Number is composed of two or more denominations of the same kind; as 4 days and 7 hours; 3 dollars, 2 cents, and 5 mills; 5 rods, 4 feet, and 6 inches.

NOTE 1. Although the quantities in the tables of the decimal system of money, weights, and measures are of different denominations, yet, as their relations are in the decimal scale, they can be written and treated as simple numbers, any denomination of the table being taken as the unit.

NOTE 2. The several parts of a compound number, though of different denominations, are yet of the same general nature; thus, 2 weeks, 3 days, and 6 hours are of like nature, and constitute a compound number; but 2 weeks, 3 miles, and quarts are unlike in their nature, and do not constitute a compound number.

231. The following tables of weights and measures are now generally used in the United States.

4. What is the cost of making a mile of road at $ 1.50 a rod?

5. How many feet is it round a room that is 16 by 12 feet?

6. How many feet in 6 rods?

7. How many yards in 48 feet?

NOTE. The units of square measure, so far as they are the same in name, are obtained by squaring (that is, taking twice as a factor) the units of the table of linear measure.

235. A Rectangle is a plane (or flat) surface bounded by four straight lines and having all its angles equal.

236. The figure is called rectangular, and the angles right angles.

237. A Square is a rectangle whose sides are equal.

238. To find the area of a rectangle.

A

C

D

Let A B C D be a rectangle whose B base AD is 5 inches in length, and whose altitude A B is 3 inches. If AD is divided into 5 equal parts and AB into 3, and lines are drawn through the points of division, the rectangle will be divided into squares, each containing 1 square inch; and the rectangle will evidently contain 5 × 3, or 15, of these squares; that is, its area =(5x3) square inches 15 square inches. = Therefore,

The area of a rectangle is the product of its length and breadth

239. The area of a rectangle divided by the length will give the breadth, and the area divided by the breadth will give the length.

240. Oral Exercises.

12. How many square inches in a rectangle 9 in. long and 7 in. wide? (See Art. 238.)

13. How many square feet in 9 square yards?

14. How many square rods in 4 acres?

15. How many acres in 400 square rods?

16. How many square yards in 72 square feet?

17. What part of an acre is 40 square rods? 80 square rods? 120 square rods?

18. How many square rods in of an acre ?

NOTE. The units of this table are obtained by cubing (that is, taking three times as a factor) the units of the table of linear measure.

245. To find the volume of a rectangular prism.

Let ABCD, E F G H be the rectangular prism whose base is a rectangle 5 inches from A to D, and 3 from A to B, and whose altitude A E is 4 inches.

E

N

F

H

D

G

the point K, one inch from A, it will evidently cut off 15 cubic inches, that is, (5 × 3 × 1) cubic inches. If, in like manner, a plane passes through M, it will cut off 15 more; and so on. That is, the rectangular prism contains (5 × 3 × 4) cubic inches = 60 cubic inches. Therefore,

The volume of a rectangular prism is equal to the product of its three dimensions.

246. The volume of a rectangular prism divided by the area of its base will give the altitude; the volume divided by the area of one end will give the length; and the volume divided by the area of one side will give the breadth or width.

247. Oral Exercises.

19. How many cubic feet in a cubical block whose edge is 2 feet? 20. How many cord feet in 48 cubic feet of wood?