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Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1900 Excerpt: ...144) + 9 = 864 sq. in. If C = volume of large cube and D = volume of small cube, But we know the volume of the small cube to be 27 cu. in.; then (1728 x 27) = C x 27, and C = (1728 x 27) + 27 = 1728 cu. in. Note.--We can see from an examination of the illustration that the surface area of the large cube must be 4 x 4 times the surface area of the small cube; that is, 16 times 54 sq. in., or 864 sq. in. Also that the volume of the large cube must be 4 x 4 x 4 times the volume of the small cube; that is, 64 times 27 cu. in., or 1728 cu. in. That is, in each case, observation shows that the principle of our rules is true. 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. 15s + 8s = 289; V289 = 17. 3. A...
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