13. How much water per minute will flow through a cylindrical water pipe 2 inches in diameter, if the water flows at the rate of 40 feet per minute? 14. How high must a tomato can that is to hold 1 quart, be made if its diameter is 4 inches? (231 cu. in. in 1 gal.) 15. An iron pipe is a cylindrical shell 2 inches in thickness. If the pipe is 10 feet long and its outer diameter is 16 inches and 1 cubic foot of iron weighs 480 pounds, what is the weight of the pipe? 16. Find the number of cubic inches in one cylinder of each of these automobiles if the stroke (altitude) of the cylinder and the bore (diameter) of the cylinder are the following number of inches. base is a polygon and whose sides are triangles. (A poly gon is a plane figure bounded by three or more straight lines. A cone has a circle for a ure I). A right cone is a cone whose (Volume times altitude) = I Area of base Spheres. The sphere is one of the most familiar solids. It is a solid whose surface at all points is equally r distant from a point within called the center. You have often called a sphere simply a "ball." Give several examples of spheres. Where r is the radius of the sphere the surface may be found by the formula (Area = 4 times square of radius) The volume may be found by the formula 1. A cone has a 7 ft. radius and is 25 feet high. How many cubic feet in it? 2. How many square yards of canvas will be required to cover the cone in example 1 if its slant height is 25.961 ft. ? 3. The base of a pyramid is a rectangle 12 X 8 inches and it is 20 inches high. What is its volume? 4. If a baseball is 2 inches in diameter, what is its area? its volume? 5. A basket ball is 10 inches in diameter. Find its surface and its volume. 6. The surface of a hemispherical (half a sphere) dome, whose diameter is 24 feet, is to be made of colored tiles, 1 inch square. How many tiles will it require to make it? 7. Find the area and volume of two spheres whose diameters are 2 and 4 inches respectively. How do the areas and volumes compare? 8. If two spheres have diameters of 6 inches and 12 inches, find their areas and their volumes. How do they compare? 9. A sphere whose diameter is 8 inches just fits into a cubical box whose edge is 8 inches. Find (1) the area of the sphere; (2) the total area of the cube; (3) the volume of the sphere; and (4) the volume of the cube. How do their areas and their volumes compare? 10. In example 9, how much of the cubic space does the sphere leave unoccupied? 11. Find the volume of a pyramid having a square base 10" on a side and an altitude of 10 inches. 12. Find the volume of a pyramid whose base is 15 cm. square and whose altitude is 10 cm. 13. Find the volume of a pyramidal church spire whose base is a hexagon having an area of 360 sq. ft. and whose altitude is 40 ft. 14. Find the lateral area of a cone whose radius is 6 inches and whose slant height is 8 inches. 15. The lateral area of a cone is 66 square inches, the slant height is 7 inches. Find the radius of the base. (Use T = 22.) Getting a Job When employers "look you up," they ask about your qualities of speed, dependability, self-reliance, honesty, and coöperation. Some day any one of these qualities or all of them will determine the contents of your pay envelope or the size of your pay check. You have heard the saying, "Honesty is the best policy." It pays to acquire also habits of speed, dependability, self-reliance, and coöperation. They all pay big dividends in money, in the esteem of friends, and in your own self-respect. Every one of these qualities can be acquired by effort and persistence. Employers do not ask whether you can acquire them. They ask whether you have made habits of them. In the following five sets of practice exercises (practice = habit) try to score 100% in the qualities of a good workman. The Habit of Speed A Time Test by Executive Committee. Are you a fast workman? Test yourself by practice in addition. Let your Executive Committee first take the test to fix a standard time for your class. While they are doing this, you copy the examples on a sheet of paper. Start adding and writing the answers when the chairman says, "Begin." When the time is up, he will say, "Stop." If you are not satisfied with the result, try again. Keep at it in out-of-class hours until you are satisfied. An Accuracy Test by Yourself. Are you a dependable workman? Test yourself by practice in subtraction. Let your Executive Committee plan how this test will be taken, how scored, and how coaching will be given. Each one should do his own scoring. |