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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 5-centimeter cube is what part of a cubic decimeter?
4. Find the solid content of a 4-decimeter cube. A 4-decimeter 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
325. MISCELLANEOUS PROBLEMS.
1. Estimate in meters the width of the lot upore whicn 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 schoolroom. 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 watet
326. TABLE OF EQUIVALENTS.
39.37 inches. Kilometer. nearly of a mile .
3280.8 + feet. Decimeter. nearly 4 inches
3.937 inches. Ar nearly to of an acre
rd. Ster a little more than cord
35.3 + cu. ft. Liter a little more than 1 liquid quart
1.056 + qt. Gram nearly 151 grains.
15.4 + grains. Kilogram nearly 27 pounds .
2.204 + lb. 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. (P. 368.)
* Every school should be provided with scales, weights, and measures.
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?
Let x= the number of decimeters in the breadth of the
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?
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 centimeters. (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 halfsecond ? (b) in the 2nd half-second ?
* In such problems the resistance of the air is not considered.
329. THE CIRCUMFERENCE OF A CIRCLE.
1. Cut a 3-inch circle from cardboard. By rolling it upon a foot rule, measure its circumference.
2. Measure the diameter of a bicycle wheel; then by rolling it upon the ground or upon the schoolroom floor, measure its circumference.
3. In a similar manner measure the diameters and the circumferences of other wheels until you are convinced that the circumference of a circle is a little more than times its diameter.
4. The circumference of a circle is nearly 34 times the diameter; more accurately, it is 3.141592 + times the diameter.
NOTE. — It is a curious fact that the diameter of a circle being given in numbers it is impossible to express in numbers its exact circumference. The circumference being given in numbers it is impossible to express in numbers its exact diameter. In other words, the exact ratio of the circumference to the diameter is not expressible.
5. Find the approximate circumference of a 5-inch circle; of a 7-inch circle; of a 10-inch circle. *
6. Find the approximate diameter of a circle that is 6 ft. in circumference. *
7. The circumference of a 6-inch circle is how many times the circumference of a 3-inch circle ?
8. The diameter of a circle whose circumference is 12 inches is what part of the diameter of a circle whose circumference is 24 inches?
* In the solution of such problems as these the pupil may use, as the approximate ratio of the circumference to the diameter, 3.14.