6. Find the continued product of 4 ft. 3 in., 5 ft. 2 in., and 6 ft. 5 in. Ans. 140 cu. ft. 10' 9" 6" 140f cu.ft.

1

PRACTICAL PROBLEMS.

1. How many square feet in a ceiling 17 ft. 3 in. long and 11 ft. 5 in. wide? Ans. 1961 sq. ft.

2. How many square feet in a pavement 12 ft. 6 in. long and 10 ft. 2 in. wide? Ans. 127 sq. ft.

3. Find the capacity of a box 3 ft. 3 in. long, 2 ft. 9 in. wide, and 1 ft. 11 in. deep. Ans. 172 cu. ft.

4. Find the content of a stick of timber 42 ft. 6 in long, 1 ft. 7 in. wide, and 1 ft. 4 in. thick.

Ans. 891 cu. ft.

5. What is the capacity of a bin 7 ft. 3 in. long, 4 ft. 2 in. wide, and 3 ft. 5 in. deep?

6. How many cords of wood

Ans. 103 cu. ft.

in a pile 13 ft. 3 in.

long, 4 ft. 2 in. wide, and 3 ft. 6 in. high?

Ans. 1 C. 651 cu. ft.

7. How many cords in a pile 20 ft. 4 in. long, 4 ft. 3 in. Ans. 3 C. 625 cu. ft.

wide, and 5 ft. 2 in. high?

8. How many cubic feet of stone in a wall 27 ft. 6 in. long, 3 ft. 3 in. thick, and 4 ft. 2 in. high ?

Ans. 37218 cu. ft.

9. What is the area of a rectangle whose length is 9 ft. 7 in., and whose breadth is 7 ft. 4 in.?

Ans. 70 sq. ft.

10. The base of a cylinder is 24 sq. ft. and its altitude Ans. 66 cu. ft.

is 2 ft. 9 in.; what is its content ?

11. What is the content of a room whose length is 18 ft.

6 in., whose breadth is 12ft. 4 in., and whose height is 10 ft. 2 in.? Ans. 2,319 cu. ft.

12. What is the area of a floor whose length is 25 ft. 3 in., and whose breadth is 20 ft. 6 in.?

Ans. 517 sq. ft.

13. What is the content of a box 1ft. 6 in. long,

1 ft. 3 in. wide, and 1 ft. 1 in. deep?

Ans. 2 cu. ft.

14. What is the content of a cube, each edge of which Ans. 37 cu. ft.

is 3 ft. 4 in.?

REVIEW QUESTIONS.

(271.) What is mensuration ? (272.) What is a polygon ? Sides? Vertices? (273.) What is the area of a polygon? (274.) Define a triangle. Its base. Its altitude. (275.) What is a parallelogram? A rectangle? (276.) What is a trapezoid? Its lower and its upper bases? Its altitude? (277.) What is a prism? Its bases? Its lateral faces? Its altitude? (278.) What is a pyramid? Its base? Its lateral faces? Its altitude? What is a frustum of a pyramid? (279.) What is a cylinder? Its bases? Its convex surface? Its altitude? (280.) What is a cone? Its base? Its convex surface? Its vertex? Its altitude? What is a frustum of a cone? (281.) What is a sphere? Its centre? A diameter? A radius? (282.) What is the relation between the sides of a right-angled triangle? (283.) What is the length of a circumference? (284.) The area of a triangle ? (285.) Of a parallelogram? (286.) Of a trapezoid? (287.) Of a circle? (288.) Of the surface of a sphere? (289.) What is the content of a parallelopipedon, prism, or cylinder? (290.) Of a pyramid or cone? (291.) Of a sphere? (292.) What is a board foot? How do you find the number of board feet in a board or plank? (293.) How is timber measured? (294.) What is the method of duodecimals? Define primes, seconds, and thirds. (295.) Give the rule for multiplication.

METRIC SYSTEM.

296. The Metric System was legalized in the United States by an Act of Congress bearing date July 28, 1866. By this act the

Meter was declared equal to 39.37 inches, which is about 1.09361 yards; the Square Meter was declared equal to 1.196 square yards; the Cubic Meter to 1.308 cubic yards; the Liter to 0.908 quarts dry measure, or to 1.0567 quarts liquid measure; and the Kilogram to 2.2046 avoirdupois pounds.

These values are only approximate, but all conversions of weights and measures from the metric to the common system, or the reverse, must be made in accordance with them in order to be legal.

297. The simplest method of reducing weights and measures from one system to the other is by means of tables.

The tables that follow have been computed from the numbers given in Art. 296, the last figure in each column being determined by the principle explained in Art. 90.

The method of using them will be explained by means of examples.

1. How many yards are there in 75.43 meters?

EXPLANATION. We take

OPERATION.

70.00 m. = 76.5528 yds.

5.00 m. =

.40 m. =

5.4681 yds.

.4374 yds.

.03 m. =

.0328 yds.

the value of 7 meters from Table I and move the decimal point one place to the right, which is equivalent to multiplying by 19; this gives the value of 70 m. We then take the value of 5 m. from the table. We next take the value of 4 m. from the table and move the decimal point one place to the left, which is equivalent to dividing by 10; this gives the value of .4 m. The value of .03 m. is found by moving the decimal point two places to the left in the

Ans. 75.43 m. = 82.4911 yds.

value of 3 m. The sum of the results is the value required.

NOTE.-For hundreds we move the decimal point two places to the right; for thousands we move it three places to the right, and so For hundredths we move it two places to the left; for thousandths we move it three places to the left, and so on.

on.

1

NOTE.-In the preceding and also in the following examples, the work is carried to 4 decimal places, the fourth figure being determined as shown in Art. 90.

3. Reduce 93.75 meters to yards. Ans. 102.5259 yds. 4. Reduce 8.67 yards to meters. Ans. 7.9278 m.

NOTE.-If necessary, let the given number be reduced to the unit of the table before commencing the transformation.

5. Reduce 72 ft. 9 in. to meters.

Ans. 24.25 yds. = 22.1742 m.

6. A city lot is 25 ft. by 100 ft.; what are its dimen

8. In 32.49 square meters how many square yards?

Ans. 38.858 sq. yds.

9. Reduce 287 sq. yds. to square meters.

Ans. 239.9664 sq. m.

10. How many square meters in a lot 100 ft. long by

25 ft. wide?

Ans. 277.7778 sq. yds. 232.2556 sq. m.