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si 4. How many rods long must a piece of land be, which is 80 rode wide, to make 1 acre ?-2. How many rods wide to mako 4 acres ? How many rods, wide to make 200, acres ?-400. 8. 410 rods.
5. How many square feet of boards are contained in the floor of a room 40 ft. 6 in. long and 10 ft. 3 in. wide? (Reduce the inches to the decimal of a foot.) A. 415,125 ft.=4154 feet.
6. How many acres are contained in the road from Boston to Providence, allowing the distance to be 40 miles, and the average width of the road 4 rods ? A. 320 acres.
7. How many square feet are contained in a board 12 inches long and 12 inches wide ?-1. 12 inches wide and 24 inches long ?-? 3 feet long ?-3. 20 feet long?-20. A. 26 feet.
8. How many square feet in a board 1 ft. 6 in. wide and 18 At. 9 in. long? A. 23,125 ft. - 28feet.
9. How many yards of carpeting, that is 14 yd. wide, will sover a floor 21 ft. 3 in. long and 13 ft. 6 in, wide ?
A, 251 yards. 10. How many feet of boards will it take to cover the walls of a house 30 ft. 6 in, wide, 40 ft. 9 in. long, and 20 ft. high? and what will they come to, at $10 per 1000 feet? A. 2–50 feet; cost $23.1.
11. How many shingles will it take to cover the roof of a barn 40 feet long, allowing the length of the rafters to be 16 A. 6 in., and 6 shingles to cover 1 square foot? what will they cost, at $1,25 per 1000?, A. 7920 shingles; cust, $.9,90.
12. What will a lot of land, 300 rods wide and 600 rods long come to, at $15 an acre: A. $16875,
13. What will a lot of land, i mile square, come to, at $20,75 per acre? A. $13280.
& LXXX. SOLID, OR CUBIC MEASURE. Q. When a block is 1 inch long, 1 inch thick, and 1 inch wide, how many solid inches is it said to contain ?
A: solid or cubic inch.
Q. How many, solid feet does a block, that is 1 foot long, 1 foot thick, and I foot wide, contain ?
A. 1 solid or cubic foot.
Q. If a block 1 foot thick, 1 foot wide, and 1 foot long, contains I solid foot, how many solid feét. does such a block that is 2 feet long contain ? 3 feet long? 5 feet, long,3. 10 feet long? 20 feet long
Q. How many solid feet does a block 2 feet long, 2 feet thick, and 1 foot wide, contain ? 2 feet wide 3 feet wide ?
Q. How many solid inches does a block 3 inches long, 2 inches wide, and I inch thick, contain ? 2 inches thick? 4 inches chick i 10 inches thick 1
S0 feet long?
Q. How, then, would you proceed, to find how many solid feet inches, &c. are coulained in a solid body?
A. Multiply the length, breadth and depth to gether.
1. How many solid feet in a block 4 feet thick, 2 feet widc, and 5 feet long? Ans. 4 X2X5= 40 solid feet.
2. How many solid or cubic feet in a block 12 incher long, 12 inches wide, and 12 inches thick?. A. 1 solid fool
Q. When a' load of wood contains 128 solid feet, what is it called ?
A. l cord. 3. How many solid feet in a pile of wood 8 feet long, 4 feet wide, and 4 feet high? A. 128,= 1 cord. How many cords of wood in a pile 8 feet long, 4 feet wide, and 8 feet high? A. 256 solid feet, = 2 cords.
Q. In common language, we say of a load of wood brought to market, if it is 8 feet long, 4 feet high, and 4 feet wide, that it is a cord, or it contains 8 feet of wood. Bui this would make 128 solid feet; what, then, is to be understood by saying of such a load of wood, that it contains & fcet of wood ? or, in common language, " there is 8 feet of it"?
A. As 16 solid feet, in any form, are } of 128 fcet, that is, $ of a cord, it was found convenient, in reckoning, to call every 16 solid feet l cord foot; then 8 such cord feet will make 128 solio feet, or 1 cord, for 8 times 16 are 128.
Q. How, then, would you bring solid feet into cord fect!
4. How many cord feet in a pile of wood 8 fect long, 2 fcet high, and I foot wide ? How many in a load 8 feet long, 2 fect high, and 2 fect wide? 8 feet long, 4 fcet wide, and 2 feet high?
5. If, in purchasing a load of wood, the se!ler should say that it contains 3 cord feet, how many solid feet must there be in the load? How many solid feet to contain 4 cord feet? 5 cord rect? 6 cord feet? 7 cord fcet ? 8 cord feet? 9 cord fcet?
6. How many cord feet in a pile of wood 8 feet long, i foot wide, and 4 feet high?
In performing inis Inst example, we multiply 4 fret (the height) by 1 fool (the width), making 4; then, this 4 by 8 feet (the longth), making 10
feord feet), = 2 cord feet, Ans. But, instead of multiplying the 4 by the 8 feet in length, and dividing by 16, we may simpiy divide by 2, without multiplying, for the divisor, 15, is 1 times as large as the multiplier, 8; consequemly, it will produce the same result as before ; thus, 4 XI=4+2 = 2 cord feet, Ans., u beture.
Q. When, then, a load of wood is 8 feet long, or contains two lengths, each 4 feet (which is the usual length of wood prepared for market), what easy method is there of finding how many cord feet sucb • &.oad contains ?
A. Multiply the height and breadth together, and divide the product by 2.
7. How much wood in a load 8 feet long, 3 feet high, and 2 feet wide? 3X2=0; 2=3 cord feet, Ans.
8. How many cord feet in a load of wood 2 feet high, 2 feet wide, and of the usual length? 3 feet high and 2 fect wide? 3 feet wide and 3 feet high? 4 feet wide and 4 feet high? 4 foet wide and 6 feet high? How many cords in a load 4 feet high, 4 feet wide ?
9. How wide must a load of wood be, which is 8 feet long and 1 foot high, to make 1 cord foot? How wide to make 2 cord feet? 3 cord feet? 6 cord feet? 10 cord feet?
10. What will a load of wood 8 fect long, 34 feet wide, and 4 feet high, cost, at $1 per foot ? The foregoing remarks and illustrations may now be embraced
in the following
Q. How do you find the contents of any solid or cube !
A. Multiply the length, breadth and depth together.
Q. When the length of wood is 8 feet, how can you find the number of cord fect it contains, withoui multiplying by 8 and dividing by 167
A. Multiply the breadth and heighit together, and divide the product by 2; the quotient will be.cord feet.
Q. How do you bring cord feet into cords ?
8 feet in length is 2 times as much wood as only 4 feet in length, hence the rogur, found as above, will has the answer in cord feet; cane is, divido by : encime, or onco by A.
Exercises for the Slate. 1. How many solid feet in a load of wood 8 feet long, 4 foort wide, and 34 feet high? 4 X 3 =14_2=7 cord feet, Ans.
2. How many feet in a load of wood 5 ft. 6 in. high, 3 A. 9 in wide, and of the usual length ? (Reduce the inches to the decimal of a foot.) A. 101%836 =10
Perform this last example by red:acing the inches of a foot to a COININOG fraction. This method, in most cascs, will be found preferable ; thus, taking the last example:
ót. 6 in. = 54 ft. =4 ; then, 3 ft 9 in.=3f ft.= 4x Hrige +2=1=1076, Ans., as before.
3. In a block 8 ft. 6 in. in length, 3 ft. 3 in. wide, and 2 ft. 9 in. thick, how many solid feet? A. Decimally, 75,96875 feet=75*} feet. By common fractions, 17x2x49 22=7531 feet, Ans., as before.
4. If a load of wood is 8 feet long and 3 feet wide, how higb must it be to make 1 cord ?
la this example, we know that the height multiplied by the width, and this product divided by 2, must make 8 cord feet, that is, 1 cord or load; kence, 8 X 2 = 16+3 = 54 feet, height, .Ans.
5. If a load of wood is 5 feet high, and 8 feet long, how wido must it be to make 2 cords?
2 cords = 16 cord feet; then, 16 X 2=32 + 5= 6 feet wide, Ans.
6. If a load of wood is 51 feet high, and 8 feet long, how wide must it be to make 3 cords ?-9.4 cords ?-12. 8 cords ?-24 A. 45 feet.
7. How many solid fect of timber in a stick 8 feet long, 18 inches thick, and 6 inches wide ?-34. 10 feet long, 12 inches thick, and I a. 3 in. wide ?-124. 20 ft. 6 in. long, 24 inches wide, and 1 f. 9 in. thick ?-714. A. 871 ft.
8. In a pile of wood 10 feet wide, 3 t. 3 in. high, and 1 milo long, how many cord feet, and how many cords?
A. 1072 cord feet = 1340% corda 9. How many tons of timber in 2 sticks, each 30 feet long, 20 inches wide, and 12 inches thick ? A. 100 feet *50=2 tons.
10. How many brieks 8 inches long, 4 inches wide, and 2 inches thick, will build a wall in front of u garden, which is ta de 240 feet long, 6 feel bigh, and I foot 6 inches tride ?
YLXXXI. Q. From what is the word duodecimals derived 1
A. From the Latin word duodecim, signifying twelve.
Q. In common decimals, we are accustomed to snppose any whole thing, as a foot, for instance, to be divided into ten equal parts; but bow is a foot divided in duodecimals ? and what are the parts called ?
A. Into twelve equal parts, called inches or primes ; and each of these parts into twelve other equal parts, called seconds; also each second into twelve equal parts, called thirds, and each third into twelve equal parts, called fourths, and 80 OD to any extent whatever.
Q. What, then, are duodecimals !
t ' the T7
Q. Now, since 12ths multiplied by 12ths make 144ths, and 11% make t'e ; also, 144ths multiplied by 12ths make 1728ths, and this make TIT; it is plain that we may write the fractions without their devominators, by making some mark to distinguish them. What marks we generally used for this purpose ?
A. 12ths, inches, or primes, are distinguished by an accent, thus; 8' signifies , 8 inches, or 8 primes; 7" =TWT, or 7 seconds; 6" =1725, or 6 thirds, &c.
Q. We have seen that 12ths multiplied by 12ths produce 14415s; what, then, is the product of 5 inches or prines) multiplied by finches) 1
d. 35“, that is, 35 seconds, or :