APPLICATIONS OF SQUARE, CUBIC, AND TIME MEASURES.

246. We propose in this chapter to give some such practical applications of Square, Cubic, and Time Measures, as the pupil is now prepared to understand; omitting for the present, those that involve square root, cube root, &c. These latter will be treated of in another place.

247. SQUARE MEASURE.

EXAMPLE 1.-How many sq. yd. in the floor of a rectangular room 5 yd. long and 4 yd. wide?

SOLUTION.-Since a floor 5 yd. long and 1 yd. wide contains 5 sq. yd., a floor 5 yd. long and 4 yd. wide contains 4 times 5 sq. yd., or 20 sq. yd. Hence to find the area of a rectangular surface (204), we have this

RULE.-Multiply the length by the width, expressed in the same denomination.

PROBLEMS.

1. How many sq. in. in a rectangular pane of glass 16 x 18 in.? How many sq. ft.? What part of a sq. yd.? 2. How many sq. ft. in a box of glass containing 60 panes, each 10 x 12 in.? Ans. 50 sq. ft.

27.55+ P.

3. How many perches in a village lot 150 ft. long and 50 ft. wide? 4. How many acres in a square farm, each of whose sides is 40 rd.

Ans. 10 A.

5. How many acres in a square piece of land measuring 6 miles on each side?

Ans. 23040 A.

EXAMPLE 2.-If a rectangular pane of glass 18 in. long, has a surface of 288 sq. in., how wide is it?

SOLUTION. EXPLANATION.-Since a pane of glass 18 in. long and 18) 288 1 in. wide contains 18 sq. in., to contain 288 sq. in. it will have to be as many inches wide as 18 sq. in. are contained times in 288 sq. in., or 16 inches wide.

16

Hence, to find one dimension of a rectangle (207), when the other dimension is given, we have this

RULE.-Divide the area by the given dimension; the quotient is the other dimension.

6. A town lot contains 2400 sq. ft. It has 20 ft. front. What is its depth?

7. A box of glass contains 50 sq. ft. How many panes 12 x 24 in. ? Ans. 25 panes.

8. How many rods in length is a rectangular farm containing 150 acres, if one end is 120 rd. in width?

9. How many yards of carpet yd. wide, will cover a floor 15 feet square? Ans. 40 yd.

10. A gentleman purchased Brussels carpet § yd. wide, at $1.75 per linear yard, to cover a room 22 feet long. The entire cost of carpet was $106.088. What was the width of the room? Ans. 15.5 ft.

11. How many yards of oil-cloth will be required to cover a hall 25 feet long and 9 feet wide; and two recesses each 6 x 7 ft.?

12. How much will it cost for blinds for 10 windows, each 7x 3 ft., at 624 per yd.? Ans. $14.58+.

248. Government Land Measure.

1. If in a Section there are 640 acres of land, how many acres are there in the E. of S. of Section 10? (See Diagram, page 191.).

2. How many in the S. E.

of E.

of S. E. of Sec. 10?
of S. W. of Sec. 21?

of E.

of S. W. 1 of Sec. 36?

3. How many in the E. 4. How many in the W. 5. A farmer purchased the N. W. of Sec. 1, Township 6, N., Range 6 E. of the 5th Principal Meridian; and sold 35 acres of it to his brother. How many acres had he left?

Ans. 125 A.

6. If he paid the usual Government pre-emption price ($1.25 per acre), and sold to his brother at the rate of $3.25 per acre, what did the part retained stand him?

Ans. $86.25.

7. If he afterwards exchanges his property for S. of the S. W. of Sec. 30, in the same Township, how much per acre does his new land cost him?

Show on the diagram the position of each 8. A speculator bought the N. of the E. of Sec. 8; he afterwards purchased the N. the N. E. 1, the S. of the W. W. of the S. of the S. W. much land did he purchase?

Ans. $1.0781.
purchase.
of the S. W. ↑

of the E. † of of the N. E. †, and the of the same section. How Ans. 160 acres.

Make a diagram showing the shape of his land.

9. He afterwards made an even exchange of two of the pieces he had purchased, so that his property was in the form of a single square. Show in how many ways this may be done.

249. Lumber Measure.

that is, it is The unit of

Lumber is reckoned by board measure; regarded as cut into boards one inch thick. board measure is a square foot, one inch thick. If a piece of lumber 1 inch thick, contains a certain number of feet, a piece with the same dimensions two inches thick, contains

twice as many feet; three inches thick, three times as many feet, &c.

The average width of a board is half the sum of the width of the ends.

EXAMPLE 1.—How many sq. ft. in a board 18 ft. long, 18 in. wide, and 1 in. thick?

SOLUTION.

EXPLANATION.-We reduce the width 18 in. to 1.5 ft. by dividing by 12; then 18 in. 1.5 linear ft. multiply 1.5 by 18, and thus obtain 27, to

which we give the name sq. ft. As the board is 1 in. thick, the surface is the product of the length and breadth, the true result being 27 sq. ft.

EXAMPLE 2.-How many feet in a plank 18 ft. long, 18 in. wide, and 14 in. thick?

SOLUTION.

EXPLANATION.-We proceed, as × 18 × 1 = 40 sq. ft. in the last example, to find the area. Since the plank is 13 times as thick as the board, it must contain 1 times as many feet 1 times 27=401.

RULE.-Multiply together the length and breadth (or average breadth) in feet; and this product by the thickness in inches.

PROBLEMS.

1. How many feet in an inch board 10 ft. long and 15 in. broad? Ans. 12 ft. 2. How many feet in a three-inch plank 10 ft. long and 15 in. broad?

3. In a log 12 ft. long and 15 in. square?
4. In a joist 20 ft. long, 10 in. broad, and 3 in. thick?

Ans. 371 ft.

Ans. 225 ft.

Ans. 50 ft.

Ans. 211 ft.

5. In a scantling 16 ft. long and 4 in. square?