12 the longest fide of the leffer bafe. 22 To the breadth of the leffer base. 220 referved number. Again, 20 the longest fide of the greater bafe, 26 16 breadth of the greater base. 416 416 220 636 40 3)25440 8480 cubic feet as above. Ex. 2. Required the folid content of a trough, in the form of a prifmoid, whose greater base is 24 inches by 30, and leffer base 20 inches by 24, the depth being 18 inches. Ans. 10728. Ex. 3. What is the content of the hopper of a mill, 4 feet by at the greater base, and 12 inches by 10 at the leffer, its depth being 4 feet? Anf. 57408 folid inches, or 33.2 feet, PROBLEM X. To find the folidity of a wedge RULE. Multiply the fum of twice the length of the bafe, and the length of the edge by the product of the height of the wedge into the breadth of the base, and of the last product will be the folidity. Note. When the length of the bafe is equal to that of the edge, the wedge is equal to one half a prifm of the fame base and altitude. EXAMPLE I. How many folid feet are in a wedge whofe bafe is 2 feet 8 inches long and 4 inches broad, its perpendicular height being 14 inches, and the length of the edge 1 foot 9 inches? Multiply the circumference by the diameter, and the product will be the furface: Or, Multiply the fquare of the diameter by 3.1416 for the furface. RULE 2. Multiply the fquare of the axis by .7854, and four times the product will be the fuperficies. EXAMPLE I. How many fquare inches will cover a globe of 6 inches dia-. meter? Note. 4 times the area of a great circle of a sphere is equal to its furface. By Ex. 2. Required the surface of a sphere, whose diameter is 5 feet 6 inches. Anf. 95.0334 fq. feet. Ex. 3. What is the furface of a ball, whofe diameter is inch? Anf. 3.1416 inches. Ex. 4. How many inches will cover a globe of 12 inches diameter ? Anf. 452.3904. Ex. 5. Required the surface of a globe of 18 inches diameter. Anf. 7.0686 fq. feet. Ex. 6. Required the fuperficies of the terraqueous globe, ita diameter being 7958 miles. And if only one fourth part of its furface be dry land, and two acres fufficient to produce food for one perfon, how many perfons can live on the earth at one time? 198956786.5824 fq. miles. Anf.49739196.6456 dry land. 15916542927 perfons. Note. A fquare mile contains 640 acres. PROBLEM PROBLEM XII, To find the folidity of a sphere. RULE I. Multiply the cube of the diameter by .5236, and the product will be the folidity. RULE 2. A globe may be confidered as composed of an infinite number of cones, whose bases are in the surface of the fphere, and common vertex in the centre; therefore the folidity of the globe may be found thus :-Multiply its surface by the diameter, and the product will give the folidity. RULE 3. Find the folidity of a cylinder, of equal diameter and altitude with the globe, and the refult will give the foli dity of the globe. es. EXAMPLE İ. Required the folidity of a globe, whose diameter is 50 inch By RULE I. 50 50 2500 50 125000 cube of the axis. 750000 375000 250000 625000 65450.000 By |