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2. The height of a room is 14 feet 10 inches, and the cir. cumference 21 feet 8 inches; how many square yards does it contain? Thus: 14--10

21-8x

9-10-8 3116

321 4 8 Then, 321.3888 feet =35.71 square-yards +. Ans.

PAVERS' WORK.

Pavers' work is done by the square yard. The content is found by multiplying the length by the breadth.

1. How many square yards in a rectangular (right-angled) court-yard, the length being 27 feet 10 inches, and breadth 14 feet 9 inches ? Ans. 410 ft. 6 in. 6 pa.=45 yds. 7 ft. 4 in. 8–8.

2. A rectangular court-yard is 64.75 feet long, and 45.5 in breadth ; what is the expense of paving at 45 cents per square yard ?

Ans. D147.30. The dimensions of the walls of a brick building being given, to

find how many bricks are required to build it.

RULE.

From thc whole circumference of the wall measured round on the outside, subtract 4 times its thickness; then multiply the remainder by the height, and that product by the thickness of the wall, will give the solid content of the whole wall, which multiplied by the number of bricks contained in a solid foot, will give the answer.

1. How many bricks 8 inches long, 4 inches wide, 2.5 inches thick, will it require to build a house 44 feet long, 40 feet wide, and 20 feet in height, the wall to be 1 foot in thickness; thus, 8X4 X2.5=80 solid inches brick, 1728:80=21.6 bricks in a solid foot : 44+40+44+40=168 feet length of wall; 168– 4=164 x 20 x 21.6=70848,0 bricks. Ans.

2. In a room of 4 walls, 2 of them measure 12.5 feet in length and 7.5 in height, and the other two sides are 14.5 feet in length, by 7.5 feet in height; required the number of square yards ; and what the plastering will amount to at 12c. per yard. Thus : 12.5 x 7.5 X2=187.5'feet; 14.5 x 7.5 X2=217.5 feet; 217.5+ 187.5=405.0-9=45 yds. X 12=D5.40. Ans. 3. How many square yards in a garden of 96 by 50 feet?

Ans. 5334 yards.

To calculate the number of shingles for a roof.

RULE.

1. Reduce the length and breadth of the space to be roofed to inches separately:

2. Divide the breadth by the average width of the shingles, and the quotient will be the number of shingles in one course.

3. Divide the length by the number of inches you intend laying the shingles or courses of the weather, and the quotient will be the number of courses.

4. Multiply the number of courses by the number of shingles in one course, and you will have the number of shingles re quired

1. Required the number of shingles for a roof 16 feet in width and 18 feet in length, the shingles to average 5 inches each in width, and the course to run 8 inches to the weather.

Thus: 16x12=192-5=38.4; 18 x 12=216--8=27x 38.4=1036.8 shingies. Ans.

MENSURATION, &c.

To measure wood, &c.

RULE.

MULTIPLY the width by the height, that product by the length, and divide by 128, and the quotient is the answer in cords.

1. Required the content, in cords, of a pile of wood 16 feet in length 5.5 feet in width, and 4.5 feet in height. 4.5 X 5.5 X 16=396.00 - 128=3 cords. Ans.

2. How many cubical feet in a piece of scantling 40 feet in length, 1.5 feet in wid.h, and .5 feet in depth ? 1.5X.5 X 40= 30.00 feet. Ans.

3. In a tier of wood 25 feet in length, 18.5 feet in width, and 7.5 feet in height, how many

cords ? Ans. 27 cords, 12 feet. 4. Required the cost of a load of wood 9 feet in length, 4.5 feet in height, and 4 feet 3 inches in width, at D5.50 per cord ?

Thus: 4.50 X 4.25 X 9=172.125; then 128:5.50 :: 172.125 : 17.39.6. Ans.

5. How many solid feet of timber in a stick 8 feet long, 10 inches thick, and 6 inches in width ?

Ans. 3} In 10 feet long, 12 inches thick, and 1 foot 3 inches wide ?

Ans. 121 6. In a pile of wood 10 feet wide, 3 feet 3 inches high, and . 1 mile long, how many cord feet, and how many cords ? 10725 cord feet=13404 cords.

7. How many cubical feet in a pile of rails 70 feet long, cut 124 feet and 14) feet high; and how many cords of wood would they make ?

To find the area of a square having equal sides.

RULE.

Multiply the side of the square into itself, and the product will be the area, or content. 1. In a garden 120 feet square, how many square yards ?

Ans. 1600.

To measure a rectangle parallelogram, or long square. A rectangle is a four-sided figure like a square, in which the sides are perpendicular to each other (right-angled), but the adjacent sides are longer and parallel.

RULE.

Multiply the length by the breadth, and the product will be the answer.

1. A. garden is 76 feet in length, and 42 feet in width ; how many square feet of ground are contained in it ?

Ans. 76 X 42=3192 feet. 2. What is the content of a field 40 rods square ?

Ans. 10 acres. 3. What is the content of a field 25 chains long by 20 chains broad?

Ans. 50 acres. 4. Required the content of a field 75 chains long and 75 chains broad?

Note.-In measuring boards, you can multiply the ler.gth ir feet by the breadth in inches, and divide by 12; the quotien will give the answer in square feet. 5. In a board 20 feet in length, 16 inches in width, how

Ans. 20 x16=320---12=263 feet.

many feet?

To measure a triangle, or to find the area A triangle is a figure bounded by three straight lines ; thus, B, A, C, is a triangle.

A When a line like A, D, is drawn, making the angle A D B square to the angle A D C, then A D is said to be perpendicular to B C, and A Dis called the altitude of the triangle. Each triangle, B AD, or D A C, is called a right-angled triangle. The

base line. side B A, or the side A C, opposite the right angle, is C

D called the hypotenuse.

hyp:

per.

B

RULE.

Multiply the base of the given triangle into half its perpendicular height, or half the base into the whole perpendicular, and the product is the answer.

1. Required the area of a triangle whose base or longest side is 32 inches, and the perpendicular height 14 inches.

Ans. 32x7 ( of 14)=224 square inches. 2. In a triangular field the base is 40 chains, and the perpendicular 15 chains; how many acres ?

Ans. 15 X 40=600:2=300-10 ch. =30 acres. 3. What is the area of a square piece of land, of which the sides are 27 chains ?

Ans. 72 acres, 3 roods, 24 poles. 4. How many acres in a piece of land 560 rods long and 32 rods wide ?

Ans, 112 acres. 5. How many acres are contained in a road 40 miles long and 4 rods wide ?

Ans. 320. 6. What will a lot of land 1 mile square come to, at D20.75 per acre ?

Ans. D13280. 7. How many yards of carpeting, that is 11 yards wide, will mover a floor 21 feet, 3 inches long, and 13 seet, 6 inches wide ?

Ans. 251 yards.

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H

radius

B

To measure a circle, area, circumference, fc. A circle is a portion of a plane bounded by a curved line, every part of which is equally distant from a certain point within, called the céntre. The curved line, A E B D, is called the circumference ; the point A C the centre; the line A B, pas

diameter sing through the centre, a diameter, and CH the radius. The circumference A E B D is 3.1416 +times

circumference greater than the diameter A B.

D Hence, if the diameter is 1, the circumserence will be 3.1416+ Also, if the diameter is known, the circumference is found by multiplying 3.1416 by the diameter. Hence the following rule:

RULE. Multiply the diameter by 3.1416, and the product will be the circumference ; or divide the circumference by 3.1416, and the quotient will be the diameter.

Note 1.-As 7 is to 22, so is the diameter to the circumference; or, as 22 is to 7, so is the circumference to the diameter. Or, more correctly:

As 113 is to 355, so is the diameter to the circumference; or as 355 is to 113, so is the circumference to the diameter.

Note 2.-The problem of “squaring the circle," as it is usually termned, has never been solved, nor can a square or any other right-lined figure, be found, that shall be equal to a given circle, as there must be a fraction in one case or the other; it is not in the power of numbers to bring them exactly alike ; the numbers used above are sufficiently correct; but the calculation may be extended to almost an indefinite number of decimals, without apparently arriving any nearer the solution of the problem.

1. If the circumference of a circle be 354, what is the diameter ? Thus : 354.000;3 1416=112.681, diameter. Ans.

2. If the diameter of a circle be 17, what is the circumference? Thus : 3.1416 X 17=53.4072, circumference. Ans.

3. If the circumference of the earth be 25000 iniles, what is the diameter ?

Ans. 7958 miles (nearly). 4. The base of a cone is a circle ; what is its diameter, when the circumference is 64 feet?

Ans. 20.3718 5. What is the circumference of a wheel whose diameter is 5 feet, 2 inches?

Ans. 16 2316. 6. If the circumference of a carriage-wheel be 16 feet, 6 inches, what is the diameter ?

Ans. 5.2521 feet,

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