« ΠροηγούμενηΣυνέχεια »
4. How many rods long must a piece of land be, which is 80 rods wide, to make 1 acre ?-2. How many rods wide to mako 4 acres? How many rods, wide to inake 200, acres ?-400. A. 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 ft. 9 in. long? A. 23,125 ft. = 284 feet.
9. How many yards of carpeting, that is 14 yd. wide, will coyer a floor 21 ft. 3 in. long and 13 ft, 6 in. wide ?
A, 25 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. 250 feet; cost $28.1. - 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 ft. 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.
FLXXX. SOLID, OR CUBIC MEASURE.
Q. When a block is 1 inch long, i inch thick, and 1 inch wide, how many solid inches is it said to contain ?
A: l solid or cubic inch.
Q. How. naany, solid feet does a block, that is 1 foot long, 1 foot taick, 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 feet does such a block that is 2 feet long contain ? 3 feet long? 5 feet long,3. 10 feet long? 20 feet long 30 feet long?
Q. Ho:v 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 thick / 10 inches thick 1
Q. Ilow, then, would you proceed, to find how many solid feet inches, &c. are contained 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 wide, and 5 feet long? Ans. 4X2X5=40 solid feet.
2. How many solid or cubic feet in a block 12 inches long, 12 inches wide, and 12 inches thick? A. 1 solid foot
Q. When a' load of wood contains 128 solid feet, what is it called ?
A. 1 cord. 3. How many solid feet in a pile of wood 8 feet long, 4 feet wide, and 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 le market, if it is 8 fect long, 4 feet ligh, and 4 feet wide, that it is a cord, or it contains 8 feet of wood. Bul this would make 128 soliu feet; what, then, is to be understood by saying of such a load of wood, that it contains 8 feet of wood ? or, in common language, “ there is 8 feet of il"?
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 solid feet, or 1 cord, for 8 times 16 are 128.
Q. How, then, would you bring solid fect into cord fect?
A. Divide by 16. . 4. How many cord feet in a pile of wood 8 fect long, 2 feet high, and I foot wide? How many in a load 8 feet long, 2 fect high, and 2 feet 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 tliere be in the load ? llow many solid feet to contain 4 cord feet? 5 cord fect? 6 cord feet? 7 cord fcet ? 8 cord feet? I cord feet?
6. How many cord feet in a pile of wood 8 feet long, 1 foot wide, and 4 feet high? a In prisforming this last example, we multiply 4 foot (the height) by 1 font (the width), naiing 4; then, this 4 by 8 foot (the length), making
beord feet) = 2 cord feet, Ans. But, instead of multiplying the 4 by the Bfnet in length, and dividing by 16, we may simpiy divide by 2, without multiplying for the divisor, 16, is times as large as the multiplier, 8; consequemly, it will produce the same result as before ; thus, 4 XI=4+2=2 cord feet, Ano., o before.
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 fiuding how many cord feet sucb . a.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? 3 X 2=6 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 Ž féet 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
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 161
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 ? • i A. Divide by 8. Note.--If the wood is only 4 feet in length, proceed as last directod; thea, B feet in length is 2 times as much wood as only 4 feet in length, henco tu result, found as above, will be the answer in cord feet; thus is, divido bys mine, 08.2000 by A.
DUODECIMALS. ILXXXI. Q. From what is the word duodeciinals derived 1
A. From the Latin word duodecim, signifying twelve.
Q. In common decimals, we are accustomed to suppose any whole thing, as a foot, for instance, to be divided into ten equal parts; bus 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 so on to any extent whatever.
Q. What, then, are duodecimals ?
What fraction of a foot is 1 second ?
. What fraction of a foot is I third ?
Q. Now, since 12ths multiplied by 12ths make 144ths, and 113 make T's; also, 144ths multiplied by 12ths make 1728ths, and to make tt; it is plain that we may write the fractions without their denominators, 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" =1ła, or 7 seconds ; 6 = 172, or 6 thirds, &c.
Q. We have seen that laiks multiplied by 12ths produce 1411hs; what, then, is the product of 5' (inches or primes) multiplied by 7 (inches) ? '
d.' 35", that is, 35 seconds, or us