1. How many square yards of plastering in a room (walls and ceiling) that is 15 ft. by 18 ft. and 12 ft. high, an allowance of 12 square yards being made for openings? NOTE. In estimating the cost of plastering, allowance is made for "openings" (windows and doors) only when they are very large in proportion to the wall to be covered. Why are plasterers unwilling to deduct the entire area of all the openings? 2. At 244 a square yard how much will it cost to plaster a room that is 17 ft. by 20 ft. and 10 feet from the floor to the ceiling, deducting 16 square yards for openings? 3. How many "double rolls" of paper will be required for the walls of a room that is 14 ft. by 16 ft. and 11 ft. high above the baseboards, if an allowance of 1 full "double roll" is made for openings? NOTE.-Wall paper is usually 18 inches wide. A "single roll" is 24 ft. long. A "double roll" is 48 ft. long. In papering a room 11 ft. high it would be safe to count on 4 full strips from each "double roll." The remnant would be valueless unless it could be used over windows or doors. Since each strip is 18 inches wide, a "double roll" will cover 72 inches (6 ft.) of wall measured horizontally. 4. At 124 a "single roll," how much will the paper cost for the walls of a room that is 12 ft. by 14 ft. and 7 ft. above the baseboards, if the area of the openings is equivalent to the surface of 2 "single rolls" of paper? 5. Find the cost, at 25¢ a square yard, of plastering the walls of a room that is 48 ft. by 60 ft. and 18 feet high, deducting 30 square yards for openings. Denominate Numbers. 336. FARM PROBLEMS. Find how many acres in— 1. A piece of land 1 rod by 160 rods. 6. A piece of land 8 rods by 80 rods. rods by 80 rods. 10. A piece of land 550 yards * by 80 rods. 11. A piece of land 12 rods by 40 rods. (c) Find the sum of the five results. 16. A piece of land 1 rod by 1 mile. 21. A piece of land of a mile long and as wide as the schoolroom. Change to rods. Denominate Numbers. 337. FARM PROBLEMS. 1. A piece of land 1 foot wide and 43560 feet long is how many acres? 2. Change 43560 feet to miles. 3. A piece of land 1 foot wide must be how many miles in length to contain 1 acre? 4. Some country roads are 66 feet wide. acres in 8 miles of such road? How many 5. How many acres in 1 mile of road that is 4 rods wide? 6. A farmer walking behind a plow that makes a furrow 1 foot wide will travel how far in plowing 1 acre? 7. A farmer walking behind a plow that makes a furrow 16 inches wide will travel how far in plowing 1 acre? 8. If a mowing machine cuts a swath that averages 4 feet in width how far does it move in cutting 1 acre? 9. If potatoes are planted in rows that are 3 feet apart (a) how many miles of row to each acre? (b) How many rods of row to each acre? (c) If 4 rods of row on the average yield 1 bushel, what is the yield per acre? 10. Strawberry plants are set in rows that are 2 feet apart. (a) How many miles of row to the acre? (b) How many rods of row to the acre? (c) How many feet of row to the acre? 11. If corn is planted in rows.3 feet apart and if the "hills" are 3 feet apart in the row, how many hills to each acre?* *Think of each "hill" as occupying a piece of land 3 ft. by 34 ft. 1. Cut one half of a circular piece of paper as indicated in the diagram. Observe that if the circle is cut into a very large number of parts and opened as shown in the figure, the circumference of the circle becomes, practically, a straight line. Note.-Imagine the circle cut into an infinite number of parts and thus opened and the circumference to be a straight line. Observe that a circle may be regarded as made up of an infinite number of triangles whose united bases equal the circumference and whose altitude equals the radius. Hence to find the area of a circle we have the following: RULE I. Multiply the circumference by of the diameter. 2. It has already been stated that if the diameter of a circle is 1, its circumference is 3.141592.* Hence the area of a circle whose diameter is 1 is (3.141592 × 1) .785398. 3. A circle whose diameter is 2, is 4 times as large as a circle whose diameter is 1; a circle whose diameter is 3, 9 times as large, etc. Hence to find the area of a circle we have also the following: RULE II. Multiply the square of the diameter by .785398. 4. The approximate area may be found by taking (or .78) of the square of the diameter. See Werner Arithmetic, Book II., page 256. * See page 229, note. 339. MISCELLANEOUS PRoblems.* 1. Find the approximate area of a circle whose diameter is 20 feet. 2. What is the area of a circle whose diameter is 1 foot? 1 yard? 1 rod? 1 mile? 3. What is the area of a circle whose diameter is 2 feet? 2 yards? 2 rods? 2 miles? 4. A horse is so fastened with a rope halter that he can feed over a circle 40 feet in diameter. Does he feed over more or less than 5 square rods? 5. Find the approximate length (in rods) of the side of a square containing 2 acres. 6. Find the approximate diameter (in rods) of a circle whose circumference is one mile. 7. Find the approximate area of the circle described in problem 6. 8. Find the approximate circumference of a circle whose diameter is 30 rods. 9. The expression "a bicycle geared to 68" means that the machine is so geared that it will move forward at each revolution of the pedal shaft as far as a 68-inch wheel would move forward at one revolution. How far does a bicycle "geared to 68" move forward at each revolution of the pedal shaft? A bicycle "geared to 70"? 10. What is the approximate circumference of the largest circle that can be drawn on the floor of a room 40 ft. by 40 ft. if at its nearest points the circumference is 2 feet from the edge of the floor? *Require the pupil to make an estimate of the answer to each problem before attempting to solve it with the aid of a pencil. |