or cones of the fame altitude with the fruftum, whereof (the greatest of the three has its bafe equal to the greater base of the fruftum; the least has its base equal to the less base of the fruftum, and the other a mean proportional be tween them. Ex. 2. What is the folidity of the fruftum of a cone, its height being 50 feet, the diameter at the greater end 20, and at the lefs end 10 feet? Anf. 9163 folid feet. Ex. 3. Required the 'folid content of the fruftum of a cone, the altitude being 9, the greater diameter 4, and the leffer 2. Anf. 65.9736. Ex. 4. Required the folidity of the fruftum of a cone, whose height is 38 inches, the diameters being 16, and 9 inches. Anf. 4785.1804. Ex. 5. What is the folidity of a log of wood, whose bases are fquares, their fides being 10 and 15 inches, and length 18 feet? Anf. 19.7916 Ex. 6. What is the folidity of the fruftum of a hexagonal pyramid, the height being 12 feet, the fide of the greater end 3 feet, and the leffer 2? Anf. 197.453472 feet. Ex. 7. Required the content of the fruftum of an octagonal pyramid, its height being 20 feet, the fides of its bafes 10 and 6 feet refpectively. Anf. 6309.14451 cubic feet. Ex. 8. Required the folidity of a mast, 11⁄2 feet diameter at the the greater base, and I foot at the leffer, its length being 72 Anf. 89.5356 cubic feet. feet. PROBLEM IX. To find the folidity of the prifmoid. RULE I. To the areas of the two ends add four times the area of the middle fection. Multiply the fum by the height, and the product will be the folidity. RULE 2. To the longeft fide of the leffer bafe add half the longeft fide of the greater base, and multiply the fum by the breadth of the leffer bafe; referve this product. Again: To the longest of the greater base add half the longeft fide of the lesser base, and multiply the fum by the breadth of the greater bafe; and to the product add the product formerly referved; multiply this fum by the height, and the product will give the folidity. EXAMPLE I. Required the folidity of a quadrilateral prifmoid, of which the shortest and longeft fides of the greater bafe are 20 and 16 feet, and the correfponding fides of the leffer bafe 12 and 10 feet, the height being 40 feet |