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TO MEASURE A CIRCLE. ART. 4. The diameter of a Circle being given, to find the Circunference.
RULE. As 7 : is to 22 : : so is the given diameter : to the circumference. Or, more exactly, As 115 : is to 355 • : &c. the diameter is found inversely.
Note.-The diameter is a right line drawn across the circle through its centre.
#XAMPLES. 1. What is the circunference of a wheel whose diam. eter is 4 feet?--Ash : 22 : : 4:12,57 the circumfe rence.
2. What is the circumference of a circic scaliane. ter is 35?-As 7 : 22 : : 35 : 110 115.--intersely as 22 : 7 :: 110 : 55, the diameter, &c. ART. 5. To find the area of a Cine's
RULE. Multiply half the aliameter by half the circumference, and the product is the area ; or if the diameter is given without the circumference, multiply the square of the diameter by ,7854 and the product will be the area.
EXAMPLES. 1. Required the area of a circle whose diameter is 12 jnches, and circumference 57,7 inches.
18,85=half the circumference.
6--half the diameter.
113,10 area in square
inches. 2. Required the area of a circular garden whose diameter is 11 rods?
7854 By the second method, 11x11 =191
Ans. 95,0354 rods. SUCTION 2. OF SOLIDS. Solids are estimated by the solid inch, solid fact, &r. 1728 of these inches, that is 12x12x12 make 1 gabi. or solid foot.
ART. 6. To measure a Cube. Definition. A cube is a solid of six equal sides, each of which is an exact square.
RULE. Multiply the side by itself, and that product by the same side, and this last product will be the solid content of the cube.
1. The side of a cubic block being 18 inches, or I foot and 6 inches, how many solid inches doth it contain ? ft. in. ft.
1 6=1,5 and 1,5X1,5X1,5=3,575 solid feet, ans. Or, 18x18x18=5852 sulid inches, and =3,375.
2. Suppose a cellar to be dug that sliall contain 12 feet every way, in length, breadth and depth ; how many solid feet of earth must be taken out to complete the same?
12x12x19=1798 solid seei, ilie Answer. ART. 7. To find the content of any regular solid of three
dimensions, length, breadth and thickness, as a piece of timber squared, whose length is more than the breadth and depth.
RULE. Multiply the breadth by the depth or thickness, and that product by the length, which gives the solid content.
1. A square piece of timber, being I foot 6 inches, or 18 inches broad, 9 inches thick, and 9 fert er 103 inches long; how many solid feet doth it contain:
1 ft. 6 in.=1,5 foot. 9 inches
Prod. 1,125*9==10,125 soliti fizilir:
in, in. in. solid in. Or, 18X9x108=17496--1728=10,125 fect.
But, in measuring timber, you may multiply the breadth in inches, and the depth in inches, and that product by the length in feet, and divide the last product by 114, w ich will give the solide content in feet, &c.
2. A piece of timber being 16 inches broad, 11 inches thick, and 20 feet long, to find the content ?
Breadth 16 inches.
the Answer. S. A piece of timber 15 inches broad, 8 inches thick, and 25 feet lony; how many solid fect doth it contain:
Ans. 20,8+feet. Arr. S. When the breaslth and thickness of a piece of
timber are given in inches, to find how much in length will make a solid foot.
NULE. Divide 1728 by the product of the breadth and depth, and the quotient will be the length making a solid foot.
1. If a piece of timber be 11 inches broad and 8 inches deep, how many inches in length will make a solid foot?
11X8=88)1728(19,6 inches, Ans. 2. If a piece of timber be 18 inches broad and 14 inches deep, how many inches in length will make a solid foot: 18x14=252 (livisor, then 252)1728(6,3 inches, Ans.
ART. 9. To measure a Cylinder. Definition.--A Cylinder is around body whose bases are circles, like a round column or stick of timber, of equal biyness from end to end.
RULE. Multiply tie sqnare of the diameter of the end by ,7854 which gives the area of the base; then multiply the area of the vise by the length, and the product will be the solid content.
What is the solid content of a round stick of timber of squal bigness from end to end, whose diameter is 18 il.. clics, and length 20 feet?
Art. 12. The length, breadth and depth of any square box being given, to tind how many bushels it will contain.
RULE. Multiply the length by the breadth, and that product by the depth, divide the last product by 2150,425 the solid inchies in a statute bushel, and the quotient will be the answer.
There is a square box, the length of its bottom is 50 inches, breadth of ditto 40 inches, and its depth 15 60 inches; how many bushels of corn will it hold?
50x40x60---2150,425=55,84+ or 55 bushels, three pecks. Ans. ART. 13. The dimensions of the walls of a brick build
ing being given, to find how many bricks are neces. sary to build it.
RULE. From the whole circumference of the wall measured round on the outside, subtract four time its thickness, then multiply the remainder by the height, and that product by the thickness of the wall, gives the solid content of the whole wall; which inultiplied by the number of bricks contained in a solid foot, gives the answer.
How many bricks S inches long, 4 inches wide, and 24 inches thick, will it take to build a house 44 fect long, 40 feet wide, and co feet high, and the walls to be one foot thick ?
8X4x2,5=: S) said inches in a brick, then 1728---80 --21,6 bricks in a solid foot. 44+407-41-440=168 feet, whicle length of wall.
-- four times the chickness.
164 remains. Multiply by 20 height.
5280 solid seet in the who.e wall Multiply by 21,6 bricks in a solid foot.