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SOLUTION.-Surface of roof equals 65×24x2=3185 sq. ft.= 31.85 squares; cost $8.75×31.85 $278.683.

2. What will it cost to pave a street 36 ft. wide and 2240 ft. long, at 30 per square foot?

Ans. $24192.

3. How many slates 12×24, exposed to the weather, will be required to cover a roof 112 ft. long and 40 ft. from eaves to ridge? Ans. 13440.

4. What will be the expense of shingling a roof 85 ft. long and 25 ft. from eaves to ridge, the shingles being worth $14.25M.? Ans. $605.62).

5. How many shingles will it take to cover a roof 65 ft. long and 30 ft. from eaves to ridge, each shingle being exposed one-third to the weather, and the first course being double? Ans. 23790.

6. Which would cost most, a brick sidewalk 74 ft. wide and 600 ft. long, at $1.25 a sq. yard, or a stone sidewalk of the same dimensions, at 18 a sq. ft.? Ans. The stone, $178.831.

CARPETING, LINING, ETC.

483. In Carpeting we take into consideration the width of the carpet, the allowance for matching the figures, and whether the strips run lengthwise or crosswise.

1. Carpets are usually 1 yd. or 2 yd. wide; but matting, oilcloth and other materials used for covering floors are of various widths.

2. To match the figures we must often turn under or cut off one of the ends. When an exact number of strips is a little too wide for the room, a part of one breadth is turned under.

Rule. Find the number of strips required, and multiply the number of yards in each strip by the number of strips. NOTE. In lining divide the whole surface by the surface of a yard of the material.

EXAMPLES FOR PRACTICE,

1. How many yards of carpet yd. wide will carpet a room 24 ft. 9 in. by 18 ft., the carpet running lengthwise? SOLUTION. It will take 8 strips each 24 ft. 9 in. long; hence it will require 243×8÷3=66 yd.

2. What will it cost to carpet lengthwise a room 33 ft.

long and 24 ft. wide, with ingrain carpet 1 yd. wide, at 75% a yard, allowing 6 in. waste for matching the figures on each piece? Ans. $67.

3. A lady wishes to carpet crosswise a parlor 33 ft. by 16 ft. 4 in. with Brussels carpet yd. wide; how many yards must she buy, allowing nothing for matching? Ans. 81 yd.

4. I wish to cover a dining-room 24 ft. long by 21 ft. wide with matting 3 ft. wide; how many yards will it take running lengthwise? how many crosswise? Ans. 48yd.; 49 yd.

5. I have a table 6 ft. long and 3 ft. 4 in. wide, which I wish to cover with a baize cloth hanging down 10 inches on each side; how many square yards do I require, and how many yards in length? Ans. 427 sq. yd.; 2§ yd.

6. My parlor has four windows, to curtain each of which it requires 8 yards of damask § yd. wide @ $1.75, lined with silk yd. wide @ 1; also 54 yds. of trimming @ $1.25, and a cornice @ $4.50; required the number of yards of silk and the whole cost of the curtains. Ans. 263 yd.; $128.163.

PAPERING.

484. Wall paper is sold only by the roll, and in estimates a part of a roll is reckoned as a whole roll.

485. A roll of American paper is commonly 8 yd. long andyd. wide.

1. Paper is now usually put up in double rolls 16 yd. long. 2. Borders and friezes are sold by the yard, and vary in width from 3 in. to 18 in.

3. On account of waste, the cost of papering a room can only be approximately estimated.

Rule.-I. Find the entire distance around the room in yards, and multiply this by 2, to fin the number of half-yards or strips. II. Divide the number of strips required for the room by the number of strips that can be cut from a roll; the quotient will be the number of rolls required.

Since there are 24 feet in a roll, if the length of the strips is 8 feet or less, strips can be cut from a roll; if between 8 ft. and 12 ft., 2 strips, etc. A double roll makes twice as many strips.

EXAMPLES FOR PRACTICE.

1. How many rolls of paper will cover the walls of a room 33 ft. long, 24 ft. wide, and 9 ft. 6 in. high?

SOLUTION.-The distance around the room is 2X(33+24)=114 ft.=38 yd.=76 half yards. Since the height is 9 ft. we can cut only 2 full strips from a roll of 24 ft. Hence the number of rolls will equal 76÷2=38 rolls.

OPERATION.

2x(33+24)=114 ft.
=38 yd.
=76 half yd.
76÷2-38 rolls.

2. What will be the cost of papering the above room at 25% a roll, including also a gilt moulding around the top of the walls at 6 a ft? Ans. $16.34.

3. What will be the cost of papering the walls and ceiling of a room 25 ft. long, 15 ft. 8 in. wide, and 91 ft. high, at $1.75 a double roll, deducting 3 rolls for doors and windows? Ans. $24.50.

4. Required the cost of papering the walls of a parlor 35. ft. long, 18 ft. wide, 10 ft. high, with base board 1 ft. wide, at $1.25 a double roll, having also a border 18 in. wide, at 45% per yard, the price including the cost of putting on the paper and border. Ans. $30.90.

NOTE. The width of base-board and border must be deducted from height of room to obtain length of strip.

5. What will be the cost of papering a room 25 ft. long, 16 ft. wide, and 9 ft. high, the base board being 6 in. wide, with paper at 45 the double roll, having a border 6 in. wide, at 9 per yard, the cost of putting on the paper being $1? Ans. $10.96.

MEASURES OF VOLUME.

486. A Volume is that which has length, breadth, and thickness or height. These three elements are called dimen sions. A volume is also called a solid.

487. By the Contents of a volume we mean the amount of space it contains. The contents are expressed by the number of times it contains a cube as a unit of measure.

THE CYLINDER.

488. A Cylinder is a round body of uniform size, with equal and parallel circles for its ends. The two circular ends are called bases.

489. The Altitude of a cylinder is the distance from the centre of one base to the centre of the other.

490. The Convex Surface of a cylinder is the surface of the curved part.

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Rule I. To find the convex surface of a cylinder, multiply the circumference of the base by the altitude.

Rule II. To find the contents of a cylinder, multiply the area of the base by the altitude.

EXAMPLES FOR PRACTICE.

1. What is the convex surface of a cylinder, the diameter of whose base is 10 inches, and whose altitude is 18 inches?

SOLUTION.-The circumference of the base equals 10 in. x 3.1416, which is 31.416 inches; multiplying by the altitude, 18, we have 565.488 square inches, the convex surface.

2. What is the surface of a marble column 20 ft. high, and 24 inches in diameter ? Ans. 125.664 sq. ft.

3. What is the length of a log of wood 18 inches in diameter, whose convex surface is 47.124 square feet?

Ans. 10 ft.

4. How many cubic feet of water will a cistern hold whose depth is 7 ft. and diameter 5 ft.? Ans. 178.1876.

5. A cistern is to be dug in a place where its diameter can only be 6 ft., but is to contain 420 cu. ft. of water; what must be the depth? Ans. 14.85+ft.

6. What will it cost to line a cylindrical cistern with tin, at 50 cents a square foot, the diameter being 6 ft. and depth 8 ft.? Ans. $89.54.

WOOD MEASURE.

491. The Measure of Wood is the cord, which is d:vided into cord feet, etc.

192. A Cord of wood is a pile 8 feet long, 4 feet wide, and 4 feet high. It contains 8 cord feet, or 128 cubic feet.

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Rule. To find the number of cords in a pile of wood, find the number of cubic feet and reduce to cord feet and cords.

EXAMPLES FOR PRACTICE.

1. How many cords in a pile of wood 32 ft. long, 8 ft. high, and 6 ft. wide?

SOLUTION.-The number of cubic feet equals 32x8x6, which equals 1536; dividing by 16, to reduce this to cord feet, we have 96 cord feet; diviaing by 8 to reduce this to cords, we have 12 cords.

2. How many cords of wood in a pile 28 ft. long, 12 ft wide, and 6 ft. high? Ans. 15 cd. 6 cd. ft. 3. If a pile of wood is 10 ft. high and 6 ft. wide, how long must it be to contain 12 cords? Ans. 25 ft. 7 in.

4. A man bought 50 cords of wood, 3 ft. long, and proposes to put it in a pile 12 ft. high; how long will the pile be? Ans. 152 ft

5. How much will a pile of wood weigh, 12 ft. long, 4 ft. wide, and 6 ft. high, of which is white oak, and the rest white pine, provided a cubic foot of white oak weighs 55 lb., and of white pine 30 lb. ? Ans. 7 tons 40 lb.

BOARDS AND TIMBER.

494. Boards and Timber are usually estimated in what are called board feet, instead of in cubic feet.

495. A Board Foot is 1 foot long, 1 foot wide, and 1 inch thick. A cubic foot, therefore, contains 12 board feet. Hence, board feet may be reduced to cubic feet by dividing by 12; and cubic feet to board feet by multiplying by 12.

496. A Standard Board, in commerce, is 1 inch thick;

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