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330. MISCELLANEOUS REVIEW.
1. Find the approximate circumference of a circle whose diameter is 3.4 meters.
2. Find the approximate diameter of a circle whose circumference is 3.4 decimeters.
3. Find the approximate diameter in yards of a circular 1-mile race track; of a half-mile track.
4. Find the approximate diameter in meters of a circular 1-kilometer race track; of a half-kilometer track.
5. A 28-inch bicycle wheel will make how many revolutions in running one mile?
6. A 70-centimeter bicycle wheel will make how many revolutions in running 1 kilometer ? *
See table on page 226 and give approximate answers to the following:
7. Forty meters are how many yards? 8. Forty yards are how many meters? 9. Forty kilometers are how many miles ? 10. Forty miles are how many kilometers? 11. Forty ars are how many acres ? 12. Forty acres are how many ars? 13. Forty sters are how many cords? 14. Forty cords are how many sters? 15. Forty liters are how many quarts ? 16. Forty quarts are how many liters ? 17. Forțy kilograms are how many pounds ? 18. Forty pounds are how many kilograms?
* The exact answer to such questions as this cannot be found: but the approxi. mation is practically correct.
NOTE. – In part to provide for ready reference, and in part to give further application of the principles presented on the preceding pages, the remaining pages of this book are devoted chiefly to denominate numbers.
331. The English and United States standard unit of length is the Imperial yard arbitrarily fixed by Act of Parliament and afterward adopted in the United States. It is about 369392 of the length of a pendulum that vibrates once a second at the level of the sea in the latitude of London. It is 36 00 of a meter.
12 inches (in.) = 1 foot (ft.).
= 1 rod.
: 1.15 + miles. 1 league (used in navigation)
= 3 knots. 1 hand (used in measuring the heights of horses) = 4 inches. 1 chain (used by civil engineers)
: 100 feet. 1 chain (used by land surveyors)
- 66 feet. 1 pace (used in measuring approximately)
- } of a rod. 1 barleycorn (used in grading length of shoes) } of an inch. 1 furlong (a term nearly obsolete)
= } of a mile.
Denominate Numbers — Linear Measure.
miles high. 2. Mt. Everest is 29000 feet, or about
miles high. 3. Commodore Dewey opened fire on the enemy at a distance of 5000 yards, or about miles.
4. My horse, measured over the front feet, is 164 hands, or - feet - inches high.
5. The vessel seemed to be about three leagues, or — miles distant.
6. On sounding, they found the depth of the water to be 15 fathoms, or feet.
7. The cruiser made 20 knots, or about miles, an hour.
8. The length of the lot was 36 paces, or about — rods. 9. 10000 feet is nearly miles. 10. 15000 feet is nearly miles. 11. 1000 yards is about
of a mile. 12. 100 feet is rods
foot. 13. 200 feet is rods feet. 14. 300 feet is rods
feet. 15. A kilometer is about rods. 16. A Civil Engineer's chain is rods
1. A seven-foot drive wheel of a locomotive makes how many revolutions to the mile ?
2. Which is the longest distance, 5 miles 319 rods 16 feet 6 inches, 5 miles 319 rods 5 yards 1 foot 6 inches, or 6 miles ?
3. Reduce 40 rd. 4 ft. 5 in. to inches.
Denominate Numbers - Surface Measure.
332. The standard unit of surface measure is a square yard which is the equivalent of a 1-yard square. This unit, like the square foot, square inch, square rod, and square mile, is derived from the corresponding unit of linear measure.
=1 square yard (sq. yd.).
=1 square rod (sq. rd.).
- 1 square rod.
=1 acre (A.). 4840 square yards
=1 acre. 43560 square feet
=1 acre. 640 acres
= 1 square mile (sq. mi.).
9 square feet
EXERCISE. 1. Show by a drawing that there are 144 square inches in a 1-foot square.
2. Show by a drawing that there are 9 square feet in a 1-yard square.
3. Show by a drawing that there are 304 square yards in a 1-rod square.
4. Estimate the number of square yards of blackboard in the room; the number of square feet of blackboard.
5. Estimate the number of square feet in the floor of the schoolroom; the number of square yards.
6. Estimate the square yards of plastering on the walls of the schoolroom.
7. Estimate the number of square rods in the schoolhouse lot. Is the lot more or less than 1 of an acre?
(P. 370.) A surface that is 9 ft. long and 1 ft. wide is a square yard though it is not itself a square. It is the equivalent of a 1-yard square.
Denominate Numbers Surface Measure. 333. In the measurement of land it is more convenient to use a decimal scale; hence the invention of the Gunter Chain. This chain is 4 rods long and is divided into 100 links.
Observe that links are hundredths of chains.
1. Land, 3 chains by 4 chains contains acres. 2. Land, 5 chains by 4 chains contains 3. Land, 3 chains by 8 chains contains acres. 4. Land, 5 chains by 7 chains contains 5. Land, 8 chains by 6 chains contains 6. Two chains 20 links equals chains. 7. Two chains 35 links equals chains. 8. Two chains 75 links equals chains. 9. Two chains 5 links equals chains. 10. Two chains 9 links equals chains. 11. Land, 4 ch. by 4.50 ch. contains 12. Land, 5 ch. by 3.20 ch. contains acres.
13. Make a rule and find the number of acres in each of the following:
(1) Land, 12 chains 35 links by 9 chains 50 links. (2) Land, 21 chains 8 links by 12 chains 30 links. (3) Land, 32 chains 25 links by 15 chains 6 links.
(a) Find the sum of the area of the ten pieces of land described on this page.
(P. 371.) TO THE TEACHER. A rod is exactly 25 links. A foot is about 11 links. Hence rods and feet can be easily changed to chains and links by regarding each 4 rods as 1 chain and each additional rod as 25 links and each additional foot as 1} links. The error in any one measurement never exceeds 2 inches. 9 rd. 12 ft. =2 chains 43 (25 +18) links.