EXERCISES 1. A rectangular solid is 12 in. by 8 in. by 6 in. What are the dimensions of a similar solid 27 times as large? 2. The diagonal of a rectangular solid is 2 in. The diagonal of another similar solid is 10 in. The surface area of the larger solid is how many times the surface area of the smaller solid? 3. The diameter of a sphere is 12 in., and its weight 96 lb. Find the weight of a sphere of the same material whose diameter is 30 in. 4. There are two cubes of the same material. The surface area of the larger is nine times that of the smaller. If the smaller cube weighs 2 lb., what is the weight of the larger? 5. A rectangular solid is 9 in. long. How much greater is the surface area of a similar solid 6 ft. long? How much greater is the volume? NOTES, HINTS, AND ANSWERS Lesson No. 1 1. Answer: 10 in. The square of the base is 62, or 36; the square of the perpendicular is 82, or 64. Now the sum of these is 100, which is equal to the square of the hypotenuse. Therefore the square root of 100, or 10, will be the length of the hypotenuse. Notice the proof of this in the following figure. 2. Answer: 17 ft. 3. Answer: 15 ft. 4. Answer: 36 in. 5. Answer: 15 ft. 152 +82289; √289=17. This is a simple right-angled triangle, with a base of 9 ft. and a perpendicular of 12 ft. 6. Answer: 20 ft. The hypotenuse and perpendicular are given; it is required to find the base. 292-212-400; √400=20. 7. Answer: AB= 15 in. AC-20 in. Draw the figure. You have two right-angled triangles. The perpendicular in each instance is 12 in. The base of one is 9 in. and of the other 16 in. Lesson No. 2 1. Answer: 279 sq. yd. 2. Answer: 324 sq. in. 3. Answer: 49 sq. ft. 4. Answer: 108 sq. ft. 31 yd. x 9 yd. 36 in. × 9 in. 7 ft. x 7 ft. Square the diagonal (hypotenuse) and square the known side, subtract, and take the square root, and we have the other side. √152-92 = √144 = 12. 5. Answer: 420 sq. ft. Similar to No. 4. 6. Answer: 52 ft. The square root of 169 is 13. This is the length of one side. The perimeter is the sum of all the sides. 7. Answer: 15 min. 40 acres = 6400 rd. The square root of 6400 is 80, the length of one side. The four sides equal 320 rd., or 1 mi. 8. Answer: 35 ft. 9. Answer: 27 ft. 192+182 + 202 = 1085. The rectangle equals three squares. The area of each square is 243 ÷ 3, or 81 sq. ft. The side of each square equals the square root of 81, or 9. 10. Answer: 16 ft. If diagonal equals √288 ft., the square of √288, or 288, equals the sum of the squares of two șides. Then the square of one side equals 288 ÷ 2, or 144. The side of the square then equals the √144, or 12. The area of the square will equal 12 x 12, or 144. Then 144 equals the area of the rectangle, one side of which is 9. Lesson No. 3 1. Answer: 54 sq. ft. (9 ×12) ÷ 2 = 54. 4. Answer: 96 sq. ft. 152 equals 225; 92 equals 81; 225-81144. The square root of 144 is 12, or the altitude AF. The base BC equals 9+7, or 16 ft. (16 x 12) 5. Answer: 7 ft. 56 divided by one-half the base. Lesson No. 4 1. Answer: 108 sq. ft. 12 x 9 = 108. = 180. (960 × 605) ÷ 4840, the number gives 120. = 2. Answer: 180 sq. ft. 3. Answer: 120 acres. of square yards in an acre, 4. Answer: 10 ft. each. 108 ÷ 9 = 12, one of the sides. Both sides equal 24. 44-24 20, the sum of the two ends. 5. Answer: 48 acres. The figure consists of two parallelograms. Their parallel sides are 80 rd. each, and the sum of their perpendiculars is 96 rd.; therefore the area in acres equals 96 × 80 divided by 160, 160 the number of square rods in an acre. Lesson No. 5 1. Answer: (a) 88 in. (b) 22 ft. (c) 11 ft. (d) 45.76 ch. (e) 88 ft. 2. Answer: (a) 42 in. (b) 35 ft. (c) 644 in. 3. Answer: 55 in. The circumference of the circle would be 220 in. This would be the perimeter of the square; therefore one side would be one-quarter of 220. 4. Answer: 7 in. The side of the square would be 11 in., and four sides, or the circumference of the circle, would be 44 in.; therefore the radius would be one-half of (44 ÷ 34). 5. Answer: 9.375 mi. The circumference of the 22 × 120 = 2640, or the 6. Answer: 30 mi. an hour. drive wheel is 7 × 31, or 22 ft. number of feet the train moves per minute. by 60 equals the number of feet per hour. to reduce to miles. This multiplied 7. Answer: (a) 154 sq. in. (b) 381 sq. in. (c) 683 sq. yd. (d) 95 sq. ft. 8. Answer: (a) 7 in. (b) 35 ft. The area divided by 34 = 1225 the square of the radius; then the square root of 1225, or 35, equals the radius. (c) 14 ft. = 9. Answer: 17 in. 10. Answer: 15 in. The area of the smaller circle multiplied by 9 equals the area of the larger circle, and this divided by 34 gives the square of the radius, or 225 sq. in. 11. Answer: 38 sq. in. The diameter is 223, or 7 in. The radius is 3 This squared and multiplied by 34 equals the area. in. 12. Answer: 88 in. The area divided by 34 gives the square of the radius. Lesson No. 6 1. Answer: 25 sq. in. The square root of 225 is 15, one side of the first square. 2. Answer: 14 in. 3. Answer: 10,800 sq. mi. 4. Answer: 168 sq. in. Note the figure. If FDE is the smaller triangle, then BDC will equal the larger, and no matter what the sides of the triangles may be, the larger |