Problems from Astronomy

1. The distance from the center of the earth to either

pole is 20,855,121 feet. How many miles is it?

2. The distance from the center of the earth to the

equator is 20,926,062 feet. What is the true equatorial

diameter of the earth?

3. Find the difference in miles between the shortest and the longest diameter of the earth.

4. Regarding the average diameter as 7913 miles, find the average circumference.

5. Find the true circumference at the equator.

6. Find the volume of the earth in cubic miles.

7. The diameter of the moon is 2160 miles. Find how many times greater the surface of the earth is than the surface of the moon.

8. Find how many times greater the volume of the earth is than the volume of the moon.

9. The diameter of the sun is about 866,000 miles. About how many times longer is the diameter of the sun than the diameter of the earth?

10. Since the two are similar bodies, about how many times the surface of the earth is the surface of the sun?

11. How many times the surface of the moon is the surface of the sun?

12. The distance of the moon from the earth is about 240,000 miles. How many times the diameter of the moon is its distance from the earth?

13. The distance of the sun from the earth is about 93,000,000 miles. How many times the diameter of the sun is its distance from the earth?

Review Problems

1. If the list price of goods is $4.00, which make the lower rate and how much, discounts of 15% and 10%, or of 10% and 15% ?

2. How much will a creditor lose on a debt of $2530, if the debtor can pay only 45 cents on a dollar?

3. The estate of a bankrupt amounted to $46,000. His liabilities were $75,950. The expense of the settlement was $430. How much could he pay on a dollar?

4. If I gain $90 by selling goods at a gain of 18%, what was the cost of the goods?

5. What is the cost of insuring property worth $15,000 for of its value, at %?

6. If the premium for insuring property at 11% is $15, for what amount is the property insured?

7. A commission merchant remits to the shipper $237.50 for the sale of goods, after having deducted his commission of 5%. For what sum were the goods sold?

8. A broker's commission for selling stock at 1% brokerage was $12.50. What was the par value of the stock

sold?

9. A clothier bought suits at $12.00 each, and marked them to sell at 25% profit. He afterwards reduced the marked price 10%. What per cent did he finally gain upon the cost?

10. A clothier bought coats at $8.00 each, and marked them to be sold at a gain of 25%. He afterward advanced his price 20%. What per cent did he finally gain upon the cost?

11. A dealer marked his goods to be sold at a gain of 20%. His price for a certain kind of cloth was 48 cents a yard. He finally sold it, however, for 45 cents a yard. What per cent did he gain?

Ratio

See p. 34.

1. What is the ratio of the volume of a 3-inch cube to that of a 15-inch cube?

2. What is the ratio of a square prism 10 inches square and 2 ft. 4 in. long to a 5-inch cube?

3. What is the ratio of a square prism a foot square and 3 ft. long to the largest cylinder that can be contained within it?

4. Find the ratio of a cone whose altitude is 15 in. and the diameter of whose base is 16 in. to a cylinder having the same base and altitude.

5. How many cones, the diameter of whose bases is 9 inches and whose altitude is 12 inches, will be equal to a sphere whose radius is 12 inches?

6. How many times the volume of a sphere whose diameter is 8 inches is that of a cylinder just large enough to contain the sphere?

7. If an agent charges 21% for selling goods, what is the ratio of the price of the goods to the amount of the commission?

8. What is the ratio of the commission to the sum remitted to the owner?

9. At the rate of 31% simple interest, in how many years will the interest upon a sum of money equal the principal ?

10. At 5% interest, what is the ratio of the principal to the interest for 2 yr. 6 mo. ?

11. A merchant bought some goods for $6000 and sold them at a gain of $750. What was the ratio of the cost to the gain? Of the gain to the selling price? Of the selling price to the cost?

Miscellaneous Problems

1. Water in freezing expands about 71%. Find the weight of a cubic foot of ice.

2. What is the specific gravity of ice?

3. If a block of ice is 20 inches thick, how many inches will the top of the block rise above the surface of the water in floating?

4. Water expands about 24 of its volume when heated from the freezing point to the boiling point. Find the weight of a cubic foot of boiling water.

5. If a cubic foot of ice should be melted, how many cubic inches of water would there be?

6. If this water should be heated to the boiling point, how many cubic inches of boiling water would there be?

7. If the water should be heated enough to convert it into steam, and the steam should be injected into a barrel of ice, how many pounds of ice would be melted, if none of the heat of the steam were wasted?

See p. 84.

8. If a pound of meat is equivalent in food value to 11⁄2 pounds of flour, how many pounds of meat are equivalent in food value to a barrel of flour?

9. When flour costs $6 a barrel, what would be the corresponding food value of a pound of meat?

10. What should be the price per barrel of flour to correspond in food value to meat at 10 cents per pound?

11. The average advance in wages per hour during the past 40 years has been about 75%. If the wages for a certain kind of work now is $3.50 a day, what was the rate paid for the same kind of work 40 years ago?

Original Problems

Make problems and solve them:

1. The average age of 10 boys in school is 15 years, 3 months, and that of 12 girls is 14 years, 4 months.

2. I bought a bill of goods at a discount of 20%, and sold them at a gain of 10%. I sold them for $44.

3. Two similar prisms are 15 inches and 10 inches long.

4. The diameters of two spheres are to each other as 13 to 29. The surface of the smaller sphere is 38 feet.

5. A block of wood floats with of its volume above the surface of the water.

6. The specific gravity of a certain kind of wood is .75.

7. By a reduction of the rate of taxation from 14 mills to 11 mills on a dollar, the tax of a certain taxpayer was reduced $24.30.

8. A man can row down stream at the rate of 8 miles an hour, and up stream at the rate of 2 miles an hour.

9. The heights of two men of similar form are 5 ft. 6 in. and 5 ft. 10 in. The smaller man weighs 130 lb.

10. The entire surface of a 9-inch cube is 486 inches. 11. The surface of one side of a cube is 81 square inches. 12. If of a number is subtracted from 3 times the number, the result is 55.

13. When water freezes it expands about 7%.

14. A cylindrical bucket 9 inches in diameter is full of water, and the water entirely freezes.

15. A block of ice 3 feet long, 21 feet wide, and 20 inches thick, is melted.