11. Suppose that A and B are two points on the opposite sides of the pond M, and we wish to find the distance between them.

Measure the distances AC and BC. Set a stake at E, a short distance from C in the line AC, and set another stake at D in the line BC, making the ratio of CD to CB equal to the ratio of CE to CA. Measure DE.

The triangles DCE and ACB are then similar and AB: DE = AC: CE.

A

B

M

D

E

12. I wish to ascertain the distance between A and B on the

opposite sides of a lake.

From C, I measure the line AC, 2000

feet, and BC, 1500 feet. I set a stake at E in line with AC, 100 feet from C, and another at D in line with BC, 75 feet from C. The distance between D and E is 50 feet.

distance between A and B?

What is the

Similar Solids

628. Solids that have exactly the same shape though they differ in volume are similar solids.

The corresponding edges or other lines of similar solids are proportional.

629. 1. Draw three cubes as in these figures, having sides proportional to 1, 2, and 3.

2. How many cubes the size of the first does the second contain? the third?

3. The volumes of cubes with sides proportional to 1, 2, and 3 are in the proportion of 1, 8, and 27, the cubes of the sides.

630. The volumes of similar solids are proportional to the cubes of their corresponding lines.

631. 1. In what proportion are the corresponding dimensions of the two similar prisms shown

here? Find the volume of the first prism

(§ 616).

By what number must you multiply this to get the volume of the second prism? What is the volume of the second prism?

Find the volume of the second prism by § 616 and compare results.

2. In what proportion are the corresponding dimensions of these two cones? How can you find the volume of the second cone from that of the first? Find the volume of each cone.

18

12

36

3. If a prism 5 inches high contains 30 cubic inches, how many cubic inches will a similar prism 10 inches high contain? What is the

4. The volume of a sphere is 96 cubic feet. volume of a sphere having a diameter half as long?

5. If the altitude of a cone that weighs 10 pounds is 2 feet, what is the altitude of a similar cone of the same material that weighs 270 pounds?

6. If a bowl 1.2 decimeters in diameter holds a certain quantity of milk, how many times this quantity will a similar bowl 1.8 decimeters in diameter hold?

7. A ball weighs 10 pounds.

Find the weight of a ball of the same material, if its diameter is 3 times as great.

8. If a column 2 decimeters in diameter contains 728 cubic decimeters, what will be the volume of a similar column 1 decimeter in diameter ?

9. How many more gallons of water can be contained in a tank 20 feet in diameter and 60 feet high than in a similar tank 40 feet high?

GENERAL REVIEW

632. 1. Mr. Kirk purchased 60 shares of a Philadelphia stock company, engaged in the manufacture of infants' hose, at $63 above par, brokerage %. How much did the stock cost him?

2. The company was capitalized at $75,000. of the stock did Mr. Kirk own?

What per cent

An order was

3. Mr. Kirk inspected the mill in detail. received for 80 doz. pairs of infants' black hose size 4; 132 doz. size 41; 248 doz. size 5; 280 doz. size 51; 236 doz. size 6; and 112 doz. size 6. How many dozen pairs were ordered? 4. He found the weights per dozen pairs to be as follows:

Find the total weight of the yarn used for these stockings, allowing a waste in manufacture of oz. per dozen pairs.

5. The price of the yarn for this order (8321⁄2 lb.) was $1.211 per pound and for dyeing it 6¢ per pound. If these two items were 62% of the total cost of the stockings, what was the cost?

6. The purchaser was given his choice of buying the 1088 dozen pairs at $1.90 per dozen, or buying size 4 at $1.60 per dozen, 4 at $1.70, 5 at $1.80, 51 at $1.90, 6 at $2, 61 at $2.10. Which was the better offer and how much?

count.

7. He accepted the first offer and paid $2067.20 less 5 % disHow much did the mill gain, the cost being $1704.96? 8. The hose for this order were the product of 32 days' work. What was the daily output of the mill?

9. At the rate of 320 dozen per day, how many dozen pairs of hose would be turned out during August, if there are 4 Sundays? how many with 4 Saturday half-holidays?

10. In the knitting room, 48 "ribbers" were used for making the legs.

of them made 810 dozen of sizes 4 and 41, in a week of 6 days; of them made 1392 dozen of sizes 5 and 51; and the rest made 612 dozen of sizes 6 and 6. Find the daily capacity of a single machine on each size.

11. At a winding machine a woman in one day wound enough yarn for 100 dozen pairs of stockings, size 4 (8 oz. plus oz. waste per doz.), and 27 lb. over. How many pounds did she wind?

12. How much did she receive for winding 56 lb. at 21 per pound?

RIBBER

13. The 45 girls employed to make and knit the feet to the legs, that day footed 330 dozen pairs, earning in all $59.40. How many dozen did each foot? at what price? how much did each earn?

14. One of the girls employed to mend stockings in the finishing room averaged 104 dozen per day and received 13 per dozen. Find her wages for a year, deducting 8 days less than 20% of the year for Sundays and holidays.

15. The mill and stock were insured for $45,000 at 1%. What was the premium?

16. The year's sales, in dozens of pairs, were:

How many dozen of each size were sold? how many white? how many black? how many colored? Find the total number.

17. Referring to exercise 4, how many pounds of yarn were used for all the white hose, adding oz. per dozen for waste?

18. This yarn, 14,062 lb., was 14% less than the total amount bought for white hose, the shrinkage being due to loss in weight during bleaching. How much of this yarn was purchased?

19. Find the total cost of the 14,240 lb. of yarn for white stockings at an average price of $1.21 per pound, and 4¢ per pound additional for bleaching.

20. How much yarn was used in the manufacture of the black and the colored hose, allowing as before oz. waste per dozen? 21. With this yarn (37,938 lb.) there was no shrinkage. Find its cost at $1.21 per pound and 6 per pound for dyeing. ¢

22. What was the cost of materials for all hose sold?

23. The cost of labor in the manufacture of stockings was 35¢ per dozen; the cost of boxes, holding dozen, was 11⁄2¢ each. Find the cost of these items for the 70,808 dozen made. during the year; the cost with $66,170.95 for materials added.

24. These expenses, $93,077.99, were $915.21 more than 85% of the entire expenses for the year, including supplies and repairs. What were the company's total expenses?

25. The average price at which these infants' hose were sold during the year was $1.90 per dozen pairs. If the discount allowed was 5%, find the net receipts from the year's sales.

26. The only other source of income was the sale of waste, amounting to oz. per dozen pairs of hose. How much money was received by selling the waste at 12 per pound?

27. The company's expenses being $108,426.80 and income $128,073.97, find the gain; the gain per cent, to the nearest tenth.