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15. Reduce of an acre to units of lower denominations.
A. X 160 == 800 sq. rd. = 1144 sq. rd.
11 sq. ft. X 144 =1594 sq. in. =1132 sq. in.
ANALYSIS.—We multiply by that number in the scale which will reduce the number to the next lower denomination, and so continue to multiply each fraction until the lowest denomination is reached.
16. Express of an acre in lower denominations.
17. What part of an acre are 100 sq. rd. ? 80 sq. rd.? 120 sq. rd. ?
18. Change g of a sq. rd. to lower denominations.
19. How many sq. in. are there in a rectangle 7 inches wide by 11 inches long?
20. How many square feet are there in a floor 8 feet long by 15 feet wide?
21. How many square yards are there in a ceiling that is 18 feet wide by 21 feet long?
42 so 22. What is the area of a square whose side is 5 feet?
23. How many square yards are there in a floor 18 feet wide by 24 feet long? How much would it cost to carpet it at $1.15 per square yard ?
24. How many yards of carpeting 1 yard wide will be required to cover a room 18 ft. long by 17 ft. wide ?
25. What will it cost to carpet a room 18 ft. long by 154 ft. wide, with carpet of a yard wide, at $1.90 per yard ?
26. If the width of a lot is 66 feet, how long must it be to contain 1 of an acre? What will be the cost of it at $3.25 per square foot ?
27. A pasture containing 10 acres had a width of 20 rods? How long was it?
28. Mr. A. sold a lot of land whose width was 20 rd. and whose length was 80 rd. at $47.25 per acre.
How much did he get for it?
29. What is the difference between 10 square feet and 10
feet square? Illustrate this by drawings. I y 30. What will be the expense of painting a roof 48 fect Wong and 22 feet wide at $.30 a square yard ?
31. What will be the cost of cementing the bottom of a cellar 45 feet by 32 feet at $.30 per square yard ? $48
32. How many yards of plastering are there in the sides of a room 18 ft. long, 17 ft. wide, and 11 ft. high? How many in the ceiling? What will be the cost of plastering at $.37 a square yard ?
33. What will be the cost of papering the side walls of the above room at $.25 per square yard ?
MEASURES OF VOLUME.
260. A Solid has length, breadth, and thickness.
261. A Cube is a solid having six equal square sides called faces. 262, A Cubic Inch is a
CUBIGENCHI solid whose sides or faces are each
a square inch.
263. A Cubic Foot is a solid whose sides are each a square foot.
264. The Volume, or Solid Contents, of any body is the number of solid units it contains.
Thus, if a solid is 4 ft. long, 3 ft. wide, and 3 ft. thick, its volume will
be 36 cubic feet. For it may be divided into 3 blocks, cach containing 12 cubic feet, making in all 36 cubic feet. That is, the number of cubic feet in each block will be equal to the product of the numbers expressing its length and breadth, and the number of blocks is equal to the number expressing the thickness. Therefore,
265. The volume of any rectangular solid is equal to the product of the numbers expressing its length, breadth, and thickness.
The length, breadth and thickness must be expressed in units of the same denomination.
1. How many cubic feet are there in a rectangular solid whose length is 3 ft., 'its breadth 2 ft., and its thickness 2 ft. ?
2. How many cubic feet are there in a cube whose dimensions are each 3 feet; or, how many cubic feet are there in a cubic yard? In a cube whose sides are 5 ft. long?
3. How many cubic inches are there in a cube whose dimensions are each 12 inches; or, how many cubic inches are there in a cubic foot ? In a cube whose sides are 10 in. long?
4. What is the volume of a cube whose sides are each 4 inches square? 9 inches square? 16 inches square?
The following are the denominations:
2. A cubic yard of earth is considered a loud.
4. Brick-layers, masons and joiners commonly make a deduction of one-half the space occupied by windows and doors in the walls of buildings.
5. In computing the contents of walls, masons and brick-layers multiply the entire distance around on the outside of the wall by the height and thickness. The corners are thus measured twice.
1. How many cubic inches are there in 2 cubic feet? In 3 cu. ft.? In 15 cu. ft.? In 32 cu. ft. ?
2. How many cubic feet are there in 2 cubic yards? In 3 cu. yd.? In 13 cu. yd. ? In 25 cu. yd. ?
3. How many cubic feet are there in 5 cords? In 8 cords?
4. How many perch of masonry are there in 418 cubic feet? What will be the cost of laying it at $1.75 per perch?
5. How many perch of masonry are there in a wall 38 feet long, 4 feet high, and ii feet thick ?
6. How many yards or loads, of earth, must be removed in digging a cellar 35 feet by 20, 8 feet deep?
7. Reduce 32 cu. ft. 114 cu. in. to cubic inches. 8. Reduce 13 cu. yd. 18 cu. ft. to cubic feet. 9. Reduce 15 perch 131 cu. ft. to cubic feet. 10. How many cubic blocks of one foot on a side can be cut from a cube that is 8 yards long on each edge ?
11. How many cubic feet in a block of marble 9 feet long, 5 feet wide, and 31 feet thick?
v 12. A man sawed a pile of wood 40 ft. long, 4 ft. wide, and
5.1 ft. high, for $1.50 per cord. How much did he earn?
13. A bin is 8 ft. long, 7 ft. wide, and 5 ft. high. How 3 many cubic feet are there in it? How many cubic inches? How
many bushels will it hold if a bushel contains 2150.4 cubic inches?
14. What will it cost to excavate a cellar 80 by 35 ft., and 8 ft. deep, at $.42 per yd.? What will be the expense of building a stone wall around it 11 ft. thick, at $3.75 a perch?
15. How many bricks will it require to build a wall 351 5 ft. long, 19 ft. high, and 3 ft. thick, allowing 22 bricks to
the cubic foot when laid ?
266. In measuring lumber, when a board is one inch thick, the number of feet board measure is obtained by multiplying the length in feet by the breadth expressed in feet.
When the lumber is more than one inch thick, the number of feet, board measure, may be obtained by multiplying the length in feet by the breadth in feet, and this product by the number expressing the inches in thickness.
When a board tapers uniformly,
How many feet are there in the following boards:
3. 10 ft. by 13 in. ?