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Metric System.

323. The primary unit of weight is the gram. This equals the weight of one cubic centimeter of pure water.

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NOTE.—The special unit for the weight of very heavy articles is the tonneau. It equals the weight of a cubic meter of pure water, or 1000 kilograms.

EXERCISE.

1. The weight of 1 liter of water is grams.
2. The weight of 6 cubic centimeters of water is
3. The weight of a cubic decimeter of water is

cubic centimeters.

4. One kilogram of water equals
5. One hektogram of water equals
6. One dekagram of water equals

CC.

cubic centimeters.

7. If the specific gravity of iron is 7.5, what is the weight of a cubic centimeter of iron?

8. If the specific gravity of cork is 1, what is the weight of a cubic decimeter of cork ?

9. If the specific gravity of oil is .9, what is the weight of a liter of oil ?

10. What is the weight of a cubic meter of stone whose specific gravity is 2.5?

11. What is the weight of a cubic decimeter of wood whose specific gravity is .8 ?

Metric System. 324. MISCELLANEOUS PROBLEMS. * 1. Find the area of a rectangular surface that is 1 meter long and 6 decimeters wide. Make a diagram of this surface upon the blackboard.

2. Find the area of a rectangular surface that is 2 decimeters long and 5 centimeters wide. Make a diagram of this surface on your slate or paper.

3. Find the solid content of a 5-centimeter cube. A 5centimeter cube is what part of a cubic decimeter ?

4. Find the solid content of a 4-decimeter cube. A 4decimeter cube is what part of a cubic meter ?

5. Find the entire surface of a 4-centimeter cube. The surface of a 4-centimeter cube is what part of a square decimeter ?

6. Find the area of a rectangular surface that is 2.4 yards by 5 yards ; of a rectangular surface that is 2.4 meters by 5 meters.

7. Which is the larger of the two surfaces described in problem 6?

8. Find the area of a rectangular surface that is 3.5 yards by 2.5 yards; of a rectangular surface that is 3.5 meters by 2.5 meters.

9. Find the volume of a rectangular solid that is 3.4 feet by 3 feet by 2 feet ; of a rectangular solid that is 3.4 meters by 3 meters by 2 meters.

10. Find the volume of a rectangular solid that is 3.5 meters by 2.3 meters by 4.6 meters.

11. What is the weight of a cubic decimeter of wood whose specific gravity is .5 ?

* Pupils should draw or image every magnitude whose dimensions are given on this page.

Metric System.

325. MISCELLANEOUS PROBLEMS.

1. Estimate in meters the width of the lot upon which the school building stands. Measure it.

2. Estimate in centimeters the width of your desk. Measure it.

3. Estimate in square centimeters the area of a sheet of paper. Measure and compute.

4. Estimate in square meters the area of the blackboard. Measure and compute.

5. Estimate the number of cubic meters of air in the school room.

Measure and compute. 6. Estimate in grams the weight of a teaspoonful of water. Weigh it. *

7. Estimate in kilograms your own weight, 8. Estimate in liters the capacity of a water pail. 9. Estimate in kilograms the weight of a gallon of water.

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NOTE 1.-A “nickel is 2 centimeters in diameter, 2 millimeters in thickness, and weighs 5 grams.

NOTE 2.-A silver dollar weighs about 25 grams.

* Every school should be provided with scales, weights, and measures.

Algebra.

327. METRIC UNITS IN ALGEBRAIC PROBLEMS. 1. I am thinking of a rectangular surface. Its length is 5 times its breadth. Its area is 45 square decimeters. How long and how wide is the surface?

NOTE.- Let x = the number of decimeters in the breadth of the surface.

2. I am thinking of a triangular surface. Its base is three times its altitude. Its area is 8.64 square meters. What is the length of its base ?

3. I am thinking of a cube whose entire surface is 150 square centimeters. What is the length of one of its edges ?

4. The perimeter of a certain rectangle is 20.4 meters. Its length is twice its breadth. (a) Find its length and breadth. (b) Find its area.

5. The difference in the weight of two lead balls is 24 grams. The united weight of the two balls is 1 kilogram. (a) Find the weight of each ball. (b) Does the heavier ball weigh more or less than 1 pound ?

6. A merchant had three pieces of lace. In the second piece there were twice as many meters as in the first. In the third piece there were 6 meters more than in the second. In the three pieces there were 106 meters. (a) How many meters in each piece? (b) Were there more or less than 43 yards in the second piece?

7. John weighs 3.6 kilograms more than Henry. Together they weigh 83.6 kilograms. (a) Find the weight of each boy. (b) Does John weigh more or less than 90 pounds ?

Algebra.

328. METRIC UNITS IN ALGEBRAIC PROBLEMS. 1. A ball rolling down a perfectly smooth and uniformly inclined plane rolls 3 times as far the 2nd second as the 1st ; 5 times as far the 3rd second as the 1st ; 7 times as far the 4th second as the first. If in 4 seconds it rolls 192 decimeters (a) how far did it roll in the 1st second ? (b) in the 4th second ? (c) Did it roll more or less than 48 inches in the first second ?

2. I am thinking of a right-triangle. Its altitude is to its base as 3 to 4. The sum of its altitude and base is 14 centi. meters. (a) Find the altitude. (b) Find the base. (c) Find the area. (d) Find the hypothenuse. (e) Is the hypothenuse more or less than 4 inches ?

3. A freely falling body falls three times as far the 2nd second of its fall as it does the 1st second. In two seconds it falls 19.6 meters. (a) How far does it fall in the 1st second ? (b) in the 2nd second ?

4. A freely falling body falls 3 times as far the 2nd minute of its fall as it does the 1st minute. In 2 minutes it falls 70560 meters. * (a) How far does it fall in the 1st minute? (b) In the 2nd minute? (c) 70560 meters equals how many kilometers ? (d) 70560 meters equals (approximately) how many miles ?

5. A freely falling body falls 3 times as far the 2nd halfsecond as it does the 1st half-second. In one second it falls 4.9 meters. (a) How far does it fall in the 1st half-second ? (b) in the 2nd half-second?

* In such problems the resistance of the air is not considered.

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