Volumes of Rectangular Solids Preparatory Exercises 1. The top layer of a box of caramels has 4 rows of 6 caramels each. (a) How many caramels are there on the top layer? (b) On the bottom layer? (c) How many caramels does the box contain if there are 3 layers? 2. How many 1-inch cubes could be placed in a box 6 inches long, 5 inches wide, 4 inches deep, inside measurement? 3. What is the capacity of a box 4 feet long, 3 feet wide, 2 feet deep? Written Exercises 1. A freight car is 32 feet long and 8 feet wide. If it is loaded with grain to the depth of 5 feet, how many cubic feet of grain does it contain? PROCESS 32 (ft.) × 8 (ft.) × 5 (ft.) = 1280 (cu. ft.). The number of cubic feet is equal to the continued product of the number of feet in the length multiplied by the number of feet in the width multiplied by the number of feet in the depth. 2. When a cubic foot will hold bushel, how many bushels of wheat are there (a) in 1280 cubic feet? (b) In 1600 cubic feet? 3. (a) How many cubic feet of corn are there in a corncrib 16 feet long, 10 feet wide, when the corn is 10 feet deep? (b) How many bushels of ear corn are there in the crib at bushel to the cubic foot? (c) If 2 bushels of corn in the ear make 1 bushel of shelled corn, how many bushels of shelled corn does the crib contain? The Romans used I, V, X, L, C, D, and M to indicate, respectively one, five, ten, fifty, one hundred, five hundred, and one thousand. Their method of expressing other numbers is shown in the following: To express numbers between ten and twenty, twenty and thirty, etc., annex to X, XX, etc., the characters representing the numbers one to nine. To express numbers between one hundred and two hundred, two hundred and three hundred, etc., annex to C, CC, CCC, etc., the characters representing the numbers from one to ninety-nine. 1. Read the following: d. MDCCVI a. XVIII b. CCCXIX c. MDCC 0. MCMX Arabic Numbers 1. Read 30 000 607 089. For convenience in reading large numbers, divide them by commas into periods of three figures each, beginning at the right. The names of the periods are given in the following To read a number begin at the highest period and read separately the number constituting each period. To each period but the last affix the name of the period. Ignore a period consisting entirely of ciphers. 89. The foregoing number is read: 30 billion, 607 thousand, NOTE.-Do not use "and" in reading whole numbers. As the billions' period is the fourth, insert three ciphers for each of the two missing periods. 2. Write 216 million, 14 thousand. Affix three ciphers for the missing ones' period. Prefix a cipher to 14 in the second period. Sight Problems 1. Find the cost of a pair of shoes at $3.50 and a hat at $1.80. Think three fifty and one eighty. Omit the words dollars and cents in giving oral answers. 2. How much change out of $10 is received by the purchaser of articles costing $5.40? 3. How old in 1915 is a boy born in 1904? 4. In 1915 a girl is 16 years old. In what year was she born? 5. A man's yearly salary was $2050. How many dollars did he save? He spent $1650. 6. Two trains start at the same time from the same point and go in opposite directions. If one goes 44 miles. in an hour, and the other 48 miles, how far apart are they (a) in 1 hour? (b) In two hours? 7. Two trains start at the same time from cities 200 miles apart and go towards each other. How far apart are they when one goes 32 miles and the other 34 miles? 8. What is the perimeter of a rectangle 28 rods long 18 rods wide? 9. A machine threshed in a day 800 bushels of oats and 430 bushels of wheat. How many bushels of grain did it thresh in a day? 10. How many men are there in an army when there are 20,000 in the infantry, 7000 in the cavalry, 3000 in the artillery, and 1000 others? 11. A barrel filled with cement weighs 404 pounds. The barrel weighs 24 pounds. What is the weight of the cement? Written Exercises 1. Mr. A bought goods during January to the following amounts: $57.81, $505, $98.87, $47.64, $0.88, $5.43, $677.42, $98.89, $6.64, and $175.53. What was the total amount of his January purchases ? 2. Add the following. Test. a. 3783 lb., 59,046 lb., 763,750 lb., 654,528 lb., 9876 lb., 605,231 lb., 67,899 lb., 8500 lb., 4095 lb., and 387 lb. b. $58, $346.75, $88.77, $1909.36, $4687.34, $504.02, $1986.35, $0.85, $675.98, and $2345.67. Addition and Subtraction 1. Mrs. B has $480. How much will she have after paying bills of $34.78, $65.43, $176.39, and $79.44? Test by covering the minuend, $480, with a piece of paper. Write on this the sum of the remainder and the subtrahends adding downwards. 2. From 12,345 take the sum of 3478, 654, 936, and 895. 3. From 6803 take the sum of 478, 654, 2176, 639, and 1234. |