6. The diameter of a sphere is 18 inches; the surface is divided into three parts by parallel planes which divide the diameter in the ratio of 1, 2, 3; find the area of the portion intercepted between the planes. Ans. 339 inches. 7. Find the curve surface of the segment of a sphere whose radius is 54 yards, and depth 31 yards. Ans. 57 yards. XXXVII. 21. To find the solidity of a sphere. Multiply the cube of the diameter by 11 and divide by Ex. Find the solidity of a sphere whose diameter is Io ft. 6 in. XXXVIII. To find the solidity of the segment of a sphere. (1) When the diameter of the sphere and the height of the segment are given: From three times the diameter subtract twice the height of the segment; multiply the difference twice by the height of the segment; then multiply by 11 and divide by 21. Ex. The diameter of a sphere is 7 ft. 3 in.; find the solidity of a segment whose height is 3 ft. 6 in. (2) When the dimensions of the segment are given: To three times the square of the radius of the base add the square of the depth; multiply the sum by the depth; then multiply by 11 and divide by 21. T. M. 6 Ex. Find the solidity of a segment of a sphere whose depth is 6 inches, and radius of the base 15 inches. 152 × 3 =675 711 6 4266 4266 3 46926 7 15642 22344 Ans. XXXIX. To find the solidity of a spherical shell. Multiply the difference of the cubes of the inner and outer diameters by 11, and divide by 21. Ex. Find the weight of a spherical shell of cast iron whose inner and outer diameters are 16 and 18 inches. XL. Given the solidity of a sphere to find the diameter. Multiply the solidity by 21, and divide by 11; then extract the cube root. Ex. Find the diameter of a sphere whose solidity is 63457. I. Find the solidity of a sphere whose diameter is 9 inches. Ans. 449'101. 2. Find the weight of a spherical shot whose diameter is 8 inches. Ans. 67 lbs. 3. Find the solidity of the segment of a sphere whose diameter is 18 inches, and height 5 inches. 4. Ans. 681*345. Find the number of gallons contained in a spherical boiler the diameter of whose brim is 4 feet, and depth 2 ft. 6 in. Ans. 149. 5. Find the solidity of a segment of a sphere the diameter of whose base is 6 ft. 10 in., and height 3 ft. 6 in. Ans. 86-663 feet. 6. Find the diameter of a sphere whose solidity is 5946 cubic inches. Ans. 22.474. Find the diameter of a sphere which contains one cubic yard. Ans. 3721 feet. 8. Find the solidity of a spherical shell whose inner and outer diameters are 12 and 15 inches. Ans. 862. 9. Find the weight of a spherical shell of cast iron whose inner and outer diameters are 8 and 10 inches. Ans. 63 lbs. 10. The diameter of a sphere is 27 inches, and the sphere is divided into three parts by two parallel planes which divide the diameter in the ratio of 2, 3, 4; find the content of each part. Ans. 1301, 42993, 47094. THE SPHEROID. If an ellipse revolve about the transverse diameter it will generate a solid called the prolate spheroid; if it revolve about the conjugate diameter, the spheroid is oblate. XLI. To find the solidity of a prolate spheroid. Multiply the square of the conjugate by the transverse diameter; then multiply by 11, and divide by 21. |