IMPORTANT APPLICATIONS. 286. CASE I.-To find the time between two dates. 1. What length of time elapsed from July 10, 1843, to Jan. 4, 1845? EXPLANATION.-Write the latter or greater date for the minuend, and the earlier for the subtrahend, giving the month its number instead of the name. Thus, since Jan. is the 1st month, we write 1 under mo. and under it write 7, as July is the 7th month. Now subtract as in compound subtraction, allowing 12 mo. to the yr. and 30 da. to the mo. Find the time from: yr. OPERATION. mo. da. 1845 1 4 1843 7 10 1 5 24 2. May 12, 1848, to June 1, 1860. Ans. 12 yr. 19 da. 3. June 1, 1861, to Oct. 20, 1872. Ans. 11 yr. 4 mo. 19 da. 4. June 15, 1846, to Jan. 10, 1848. Ans. 1 yr. 6 mo. 25 da. 5. April 20, 1868, to Aug. 1, 1869. Ans. 1 yr. 3 mo. 11 da. 9, 1868, and Harry Sept. 6. Henry was born March 15, 1875; how much older is Henry than Harry? 7. A note dated July 15, 1882; how long did it run? Ans. 7 yr. 6 mo. 6 da. 1879, was paid May 21, Ans. 2 yr. 10 mo. 6 da. To what age did the following live: 8. Washington, born Feb. 22, 1732; died Dec. 14, 1799? 9. Jefferson, born April 2, 1743; died July 4, 1826? 10. Lincoln, born Feb. 12, 1809; died April 15, 1865? 11. Calhoun, born March 18, 1782; died March 31, 1850? 12. Webster, born Jan. 18, 1782; died Oct. 24, 1852? 13. Clay, born April 12, 1777; died June 29, 1852? 287. CASE II.-To find the area of rectangular surfaces. A rectangular surface is a surface in the shape of a sheet of paper, or of an ordinary square cornered garden of four sides. RULE.-Multiply the length by the width, expressed in like units. i. What is the area of a floor 18 ft. long and 12 ft. wide? Ans. 216 sq. ft., or 24 sq. yd. 2. What is the area of a rectangular garden 88 yd. long and 55 yd. wide? Ans. 4840 sq. yd., or 1 A. 3. What is the area of a rectangular field 35 ch. long and 24 ch. wide? Ans. 840 sq. ch., or 84 A. 4. How many acres in a meadow 17 ch. long and 12 ch. wide? Ans. 20.4 A. 5. How many acres in a field 60 rd. long and 44 rd. wide? Ans. 16 A. 6. How many yards of carpeting 3 ft. wide will it take to cover a floor 20 ft. long and 15 ft. wide? We divide the number of sq. ft., 300, by the width of the carpet, 3 ft., which gives the length of the carpet, 100 ft., and this divided by 3 gives 33 yd. OPERATION. = 20 X 15 300 3003100 100 ft. 3331 yd. 7. How many yards of carpeting 4 ft. wide will it take to cover a floor 22 ft. long and 18 ft. wide? Ans. 33 yd. 288. CASE III.-To find the volume of a rectangular solid. A rectangular solid is a solid in the shape of an ordinary goods-box, or of a room. The figure represents a rectangular solid 5 ft. long, 4 ft. high, 3 ft. wide, and evidently contains 5X4X3=60 cu. ft. 60 cu. ft. is called its volume. Hence, RULE.-Multiply the length, width, and height together. NOTE. The dimensions must be expressed in terms of the same measure. 1. What is the volume of a rectangular box 6 ft. long, 3 ft. wide, and 5 ft. high? Ans. 90 cu. ft. 2. What is the volume of a room 20 ft. long, 18 ft. wide, and 12 ft. high? Ans. 4320 cu. ft., or 160 cu. yd. 3. How many cubic feet in a marble slab 60 in. long, 24 in. wide, and 6 in. thick? Ans. 5 cu. ft. 4. How many cubic yards of coal in a pile 18 ft. long. 10 ft. wide, and 7 ft. high? Ans. 463 cu. yd. 5. How many cubic feet of corn in a crib 20 ft. long, and 12 ft. wide, the corn being 5 feet deep in the crib? Ans. 1320 cu. ft. 6. How many cords of wood in a pile 20 ft. long, 12 ft. wide, and 6 ft. high? Ans. 114 cords. OPERATION. 20 × 12×6 — 114. 128 How many cords in a pile of wood: 7. 24 ft. long, 8 ft. wide, and 4 ft. high? 8. 18 ft. long, 6 ft. wide, and 8 ft. high? Ans. 6 c. Ans. 63 c. 289. CASE IV.-To find the number of gallons in a rectangular box or tank. 1. How many gallons of water will a tank hold which is 6 ft. long, 5 ft. wide, and 8 ft. high? OPERATION. 6×5X8X7=1800 gal. Ans. EXPLANATION. -Since there are 231 cu. in. in one gallon, and 1728 cu. in. in one cubic foot, 1 cu. ft.=172 gal. or about 71 gal. Hence, the RULE.-Multiply the number of cu. ft. by 74. 2. How many gallons of molasses will a box hold which is 4 ft. long, 2 ft. wide, and 9 in. ( 3. A box is 3 ft. long, 2 ft. wide, 8 in. and is full of honey; how much honey is ( ft.) high? Ans. 45 gal. ft.) high, in the box? Ans. 30 gal. What is the capacity of a tank which is: 4. 6 ft. long, 4 ft. wide, and 10 ft. high? Ans. 1800 gal. 5. 4 ft. long, 4 ft. wide, and 9 ft. high? Ans. 1080 gal. 6. 5 ft. square at the bottom and 7 ft. high? Ans. 1312 gal. 7. 3 ft. square at the bottom and 6 ft. high? Ans. 405 How much milk will a box hold which is: 8. 14 ft. long, 1 ft. wide, and ft. high? Ans. 74 gal. 9. 13 ft. long, 1 ft. wide, and 6 in. high? Ans. 7 gal. 10. 9 in. long, 8 in. wide, and 4 in. deep? Ans. 11 gal. 290. CASE V.-To find the number of bushels in a rectangular box, bin, or granary. 1. How many bushels of wheat will a box hold which is 5 ft. long, 4 feet wide, and 3 ft. deep? OPERATION. 5X4X3X.848.0 48 bu. EXPLANATION.-Since there are 2150.4 cu. in. in one bushel, and 1728 cu. in. in one cubic foot, then 1 cu. ft. about .8 bu. Hence, the RULE.-Multiply the number of cu. ft. by .8. 1728 18 bu.= 2. Which is 6 ft. long, 5 ft. wide, and 2 ft. high? Ans. 60 bu. 3. Which is 6 ft. long, 4 ft. wide, and 2 ft deep? Ans. 57% bu. 4. Which is 5 ft. long, 33 ft. wide, and 2 ft. deep? Ans. 40 bu. 5. Which is 7 ft. long, 23 feet wide, and 33 ft. deep? Ans. 531 bu. 291. CASE VI.-To find the number of board feet in boards or planks. A Board Foot is used in measuring boards, planks, and sawed timber generally. It is 1 foot long, 1 foot wide, and 1 inch thick, and contains 144 cu. in. |