The volume or contents of a prism or a cylinder is equal to the area of one of the bases multiplied by the altitude.

[Use pencil only when needed.]

1. Area of base, 12 sq. ft.; altitude, 6 ft.

2. Area of base, 17.5 sq. in.; altitude, 12 in.

3. Length of rectangular base, 14 in.; width, 6 in.; altitude of prism, 5 in.

4. What is the contents of a cylinder whose radius is 10 ft. and whose altitude is 6 ft.? (Area of base 3.1416 x the square of the radius.)

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5. Given a cylinder with radius, 8 in., and altitude, 10 in.; find its volume.

[With pencil.]

6. Twelve cubic feet of air weigh a pound. Find the weight of the air in your schoolroom.

7. How much water is there in a cistern whose diameter is 8 ft., when the depth of water is 12 ft. 9 in.? How many gallons of water does it contain? (1 gallon 231 cu. in.)

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8. At 150 lb. to the cubic foot, find the weight of a rectangular paving stone with these dimensions: 33 ft. by 4 ft. by 5 in.

9. A bushel contains 2150 cu. in. How many bushels of oats can be put into a bin whose base measures 6 ft. by 4 ft., and whose altitude is 5 ft.?

10. What is the capacity of a gas tank whose diameter is 70 ft., and whose altitude is 45 ft. 9 in.?

*11. If a cubic foot of silage weighs 35 lb., how many tons of silage can be put into a silo 20 ft. deep, the area of whose base is 600 sq. ft.? If each cow eats 40 lb. of silage a day, how long will the silage last a herd of 45 cows?

*12. Measure a prism or a cylinder at home. Make and solve a problem based on your measurements.

A pile of wood, 8 ft. long, 4 ft. wide, and 4 ft. high (128 cu. ft.) is called a cord.

[With pencil.]

1. How many cords of wood can be piled into a shed, 18 ft. long, 8 ft. wide, and 10 ft. high?

He

2. Mr. Peterson cut 17 cords of wood from his woodland. paid $3.25 a cord for having it sawed and split, and sold it at $2.50 for a quarter-cord. How much did he make on the wood? *3. Make and solve five other problems about cords of wood. Use local prices.

IV. CONES AND PYRAMIDS

A solid having a circle as a base and a convex surface tapering uniformly to a point is called a cone.

A solid whose base is a polygon and whose sides are triangles terminating in a common point is called a pyramid.

Cone

Pyramid

Give examples of objects that you have seen that are cones or pyramids.

V. FINDING THE VOLUME OF CONES AND PYRAMIDS

If you should make a hollow cone and a hollow cylinder with the same base and the same altitude, you would find that you could exactly fill the cylinder by emptying the cone, filled with sand, into the cylinder three times. The cone holds one third as much as the cylinder.

Similarly, we find that a pyramid holds one third as much as a prism having the same base and altitude.

Since the volume of a cylinder or a prism is equal to the product of the area of the base and the altitude, we conclude that

The volume of a cone or a pyramid is equal to one third the product of the area of the base and the altitude.

[Use pencil only when necessary.]

1. What is the volume of a cone the diameter of whose base is 6 ft. and whose altitude is 7 ft.?

2. Given the area of the base of a pyramid, 250 sq. in., and the altitude, 36 in., find its volume.

3. Find the volume of a pile of sand in the shape of a cone, the area of whose base is 216 sq. ft. and whose height measures 5 ft. 4 in.

4. To gain an idea of the immensity of the pyramid of Cheops in Egypt, find its volume. Its square base is 746 feet on a side, and its height is 480 ft.

*5. Measure some object having the shape of a cone or a pyramid; then make and solve a problem based on your measurements.

39. Measuring Heat Expansion

1. Why does a blacksmith heat a new tire that he wishes to fit on to a wheel?

2. Why are spaces left between the ends of railroad rails?

3. What happens to the mercury column in a thermometer when the air is very warm? Put your hand on the bulb of a thermometer and observe the result.

About 200 years ago, a man named Fahrenheit invented the thermometer. He put a small tube, marked off into equal spaces, called degrees, which he had filled with mercury, into melting ice and marked the height of the mercury column, 32°, as the freezing point. Then he put it into boiling water and marked the height of the mercury column, 212°, as the boiling point.

[Without pencil.]

4. How many degrees are there between the boiling point and the freezing point of water?

We use the sign (+) to indicate a number of degrees "above zero," and the sign (−) to indicate a number of degrees "below zero."

In the following readings, give the rise or fall in temperature:

14. The readings for four successive days were as follows: -4°; -2°; -5°; -6°. Give the average temperature for the four readings.

1

The Centigrade 1 thermometer is commonly used in scientific work. The freezing point (32° F) on this thermometer is marked zero; and the boiling point (212° F), 100 degrees. Degrees below the freezing point are indicated by the minus (-) sign. Since 100° C 180° F (212° 32° 180°), to change Fahrenheit degrees to Centigrade, subtract 32° (since 32° F is 0° C) and multiply by § (188). To change Centigrade degrees to Fahrenheit, multiply by (188) and add 32°.

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[Use pencil only when needed.]

15. 1° C is how many degrees Fahrenheit?

16. Change 122° F to Centigrade. 17. Change 212° F to Centigrade. 18. Change 50° C to Fahrenheit.

19. Change 60° C to Fahrenheit.

20. The temperature of a liquid is 73° C. How

many degrees Fahrenheit is this?

*21. Make a graph on the blackboard, showing the temperature in Centigrade degrees, each day at a given hour for a week.

*22. A piece of steel will expand .0012 times its length when heated from 32° F to 212° F. If a railway track is laid when the tem

1 Centigrade means one hundred degrees.