Drill Work

In adding these columns combine at a glance groups of figures whose sum is 10, and thus add by 10's.

A cone is a solid that has a circle for its base, and that terminates in a point at its upper extremity. A cone may be regarded as a pyramid whose lateral surface is composed of a large number of very small triangles. If we could divide the lateral surface of a cone on one line of its slant height and spread it out upon a plane surface, what form would it assume?

1. Find the lateral surface of a cone the circumference of whose base is 25 inches, and whose slant height is 14 inches.

2. Find the diameter of the base of a cone whose circumference is 62.832 inches.

3. What is the circumference of the base of a cone, if the radius of the base is 24.15 feet?

4. Find the lateral surface of a cone, the diameter of whose base is 32 inches, and whose slant height is 6 feet.

Statistics

1. The population of the United States from 1870 to 1900 increased from 38,500,000 to about 76,000,000. What has been the average increase for each year?

2. In 1870 there were 5871 newspapers and other periodicals published. In 1900 there were about 21,000. How many times did the number multiply during the period?

3. How many people were there for each paper published in 1870 ?

4. How many less people were there for each paper published in 1900 than in 1870?

5. In 1870 there were 28,492 post offices. people were there for each post office?

How many

How many

6. In 1900 there were 75,000 post offices. less people were there for each post office in 1900 than in 1870 ?

7. In 1870, 9,000,000 telegraphic messages were sent, and in 1899 about 77,000,000. Find whether the increase in the number of telegraphic messages was greater or less, proportionately, than the increase in population.

8. In 1870, 1,630,000 people in the country had deposited in the savings banks $550,000,000. What was the average size of these deposits?

9. How much did this amount average for each person in the total population?

10. In 1900, 5,687,000 persons had $2,230,000,000 deposited in institutions for savings. What was the average then for each depositor?

11. Find how much the average amount for each person of the population increased in the 30 years.

Review Problems

1. The longitude of Boston is 71° 3′ 30′′ W., and that of New York 74° 0' 3" W. What is the true difference in time?

2. The longitude of San Francisco is 122° 26′ 15′′ W. What is the true difference in time between New York and San Francisco?

3. What is the true difference in time between Boston and San Francisco?

4. Honolulu is 157° 52′ 0′′ W. In sailing from San Francisco to Honolulu how much must a watch be set back?

5. If a circular piece of paper 20 inches in diameter is cut in halves, and one half is formed into a cone, what will be the slant height of the cone?

6. What will be the circumference of the base of the cone?

7. What will be the diameter of the base?

8. What will be the convex surface?

9. If a circular piece of paper 24 inches in diameter is cut in quarters, and one of the quarters is formed into a cone, what will be the slant height of the cone?

10. What will be the diameter of the base?

11. What will be the convex surface?

12. If from a circular piece of paper whose circumference is 30 inches a section is removed by cutting from the circumference to the center so as to remove 6 inches of the circumference, and the edges are brought together so as to form a cone, what will be the diameter of the base of the cone?

13. What will be the convex surface of the cone?

Which of the three classes of levers are pump handles? Nut crackers? Shears?

1. If it is 25 inches from the end of the handle of a pump to the bolt by which it is fastened, and 5 inches from this bolt to the piston rod, how many pounds of pressure must be applied at the end of the handle to raise 100 lb. of water?

2. If the entire length of the pump handle is 36 inches and the shorter part is 8 inches, how many pounds of water can be raised by a child who can pull down 35 lb. upon the handle?

3. In a nut cracker, which is 6 inches long from the joint to the point where the fingers press, the nut is placed 2 inches from the joint. How much pressure can be applied to the nut by pinching 20 lb.?

4. How many pounds could be applied, if the nut were 11⁄2 inches from the joint?