Review Problems 1. Cloth which cost $1.20 a yard was sold at an advance of 33%. What was the selling price? 2. A lot of 400 barrels of flour worth $5 a barrel was insured for of its value at %. What was the premium? & 3. A collector collected $460 on a commission of 5%. What sum did he pay to his employer? 4. How many men will it take to do a piece of work in 10 days which 12 men can do in 15 days? 5. What must be the length of a piece of land 64 rd. wide in order that it may contain the same number of acres as a piece of land 200 rd. long and 80 rd. wide? 6. How many yards of carpet cover the same space as a carpet yards long? of a yard wide will of a yard wide and 30 7. What is the entire surface of a square pyramid the perimeter of whose base is 20 ft. and whose slant height is 50 ft.? 8. What is the volume of a square pyramid the perimeter of whose base is 36 ft. and whose altitude is 32 ft. 8 in.? 9. An ancient historian reported that the side of the base of the Great Pyramid in Egypt was 883 pedes, or Roman feet. Two pedes make a cubit, and a cubit is equal to 20.7 inches. What was the length of the side of the pyramid? 10. The Great Pyramid is a square pyramid, and is 450 feet high. If we take 760 feet as the length of its base, what is the distance around it? 11. How many miles of wall 10 ft. high and 1 ft. thick could be made with the stone contained in it? Buoyancy of Water-Specific Gravity See pp. 23, 99. Water, by its buoyant force, presses upward against an object as much as the weight of the water displaced by the object, so that the object will weigh so much the less in water than in the air. If an object weighs 500 ounces less in water than in the air, the water which it has displaced would weigh 500 ounces; hence one half of a cubic foot of water must have been displaced. . 1. What is the weight of a cubical block a foot long which will just float in water without rising above the surface? 2. If the block were twice as heavy as water, how much would it weigh if attached to the scale by a string and suspended in water ? 3. If an object weighs as much in the water as in the air, what is its specific gravity? 4. If an object weighs more in the air than in water, what is its specific gravity? 5. If a glass is exactly full of water and an object is lowered into it, how much water will overflow? 6. If the water which overflows weighs 20 ounces, and the object weighs 50 ounces when suspended in water, what is the entire weight of the object? 7. What is the specific gravity of the object? 8. If an object, when lowered into a glass full of water, causes of a cubic foot of water to overflow, and weighs 10 pounds when suspended in the water, what is its specific gravity? Review Problems 1. If I insure my life for $4000, and the premium is 3% quarterly, how much will the premium amount to in 3 years? 2. A man whose property is assessed for $6000 is taxed 12 mills on a dollar. How much is his tax? $500. SPRINGFIELD, ILL., March 15, 1899. For value received, I promise to pay to the order of James Haskell, Five Hundred Dollars, on demand, with interest at 5%. JOSEPH EVERETT. 3. Find how much was due on the above note Jan. 1, 1900. 4. Find how much would have been due if it had not been paid until Aug. 23, 1900. 5. What is the interest of $560 from Sept. 19, 1895, to Apr. 1, 1898, at 4%? 6. What is the amount of $275 with interest for 1 yr. 7 mo. 13 da., at 51% ? 7. What sum of money will produce $106.08 of interest in 6 yr. 3 mo. 15 da., at 41%? 8. What is the rate when the amount of $255 for 2 yr. 7 mo. 6 da. is $288.15? 9. In what time will $420 gain $37.80 at 4%? 10. What is the volume of a square prism one end of which is 14 in. square, and whose altitude is 27 in. ? 11. What is the volume of a square pyramid whose base is 17 in. square, and whose altitude is 39 in.? 12. What is the lateral surface of a triangular pyramid each side of whose base is 8 ft. 9 in. and whose slant height is 12 ft. 9 in.? Construction See pp. 102, 123. 1. Construct a triangle with an angle of 48°, a side 3 inches long, and an altitude of 4 inches. 2. Construct a right triangle with a base 2 inches long and an hypotenuse 4 inches long. 3. Construct a parallelogram with a side 31 inches long and an angle of 52°. Upon the same base construct a rectangle which will have the same area as the parallelogram. Find the area. 4. Make a triangle with a base 3 inches long and an angle of 65°. Regarding this triangle as a part of a parallelogram, complete the parallelogram. Upon the same base make a rectangle whose area will be equal to that of the parallelogram. Find the area of the parallelogram and of the triangle. 5. Make a trapezoid with a base 4 inches long. Make a rectangle upon the trapezoid which will have the same area as the trapezoid. Find the area. 6. Make a triangle with a base 4 inches long and an altitude 3 inches. Make another triangle with a base 3 inches long which shall be equal in area to the first triangle. 7. Make a regular pentagon with a side 11⁄2 inches long. Find the center. Divide the pentagon into triangles. Find the area. 8. Make a regular hexagon with a side 11⁄2 inches long. Find the center. Divide the hexagon into triangles. Find the area. 9. Make a square 23 inches long. Inscribe a circle. Find the area of the circle, and of the part of the square outside the circle. Original Problems Make problems and give answers: 1. One of the two equal means in a proportion is 12. One of the extremes is 6. 2. One of the extremes in a proportion is 8 and the other is 18. 3. 4 men can dig a ditch 7 rods long in a day. 4. A pipe 4 inches in diameter and 12 feet long is filled with water. 5. The moon revolves around the earth in 27 da. 7 hr. 43 min. 11 sec. 6. The planet Uranus revolves around the sun in 30,686.8 days. 7. The distance of Uranus from the sun is 1,753,869,000 miles. 8. 5 men can build a piece of fence in 3 days. 9. One rectangle is 12 feet long and 10 feet wide. Another is 8 feet wide. 10. 10 acres of grass are sufficient for three cows. 11. In carrying a barometer up a mountain to a certain height it falls 3 inches. 12. The base of a prism contains 12 square feet, and its altitude is 6 feet. 13. The diameter of a cylinder is 26 inches. 14. The base of a square pyramid is 8 feet square, and the altitude is 15 feet. 15. A cylindrical standpipe 20 feet in diameter is filled with water to a depth of 24 feet. 16. A cubic foot of marble weighs 2800 ounces. 17. The specific gravity of sea water is about 1.025. |
