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Ex. 2. What is the folidity of the frustum of a cone, its height being 50 feet, the diameter at the greater end 20, and at the less end 10 feet? Anf. 9163 folid feet.

Ex. 3. Required the 'folid content of the frustum 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 frustum of a cone, whose height is 38 inches, the diameters being 16, and 9 inches.

Ans. 4785.1804

Ex. 5. What is the folidity of a log of wood, whose bafes are squares, their fides being 10 and 15 inches, and length 18 feet? Anf. 19.7916

Ex. 6. What is the folidity of the frustum of a hexagonal pyramid, the height being 12 feet, the fide of the greater end 3 feet, and the leffer 2? Ans. 197-453472 feet.

Ex. 7. Required the content of the frustum 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, feet diameter at

the

the greater base, and I foot at the leffer, its length being 72 feet. Anf. 89.5356 cubic feet.

PROBLEM IX.

To find the folidity of the prismoid.

RULE I.

To the areas of the two ends add four times the area of the middle section. Multiply the sum by the height, and the product will be the folidity.

RULE 2. To the longest side of the leffer base add half the longest fide of the greater base, and multiply the sum by the breadth of the leffer base; reserve this product.

Again: To the longest of the greater base add half the longest side of the lesser base, and multiply the sum by the breadth of the greater base; and to the product add the product formerly referved; multiply this sum by the height, and + the product will give the solidity.

EXAMPLE I.

Required the folidity of a quadrilateral prismoid, of which the shortest and longest fides of the greater base are 20 and 16 feet, and the corresponding fides of the leffer bafe 12 and 10 feet, the height being 40 feet

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32

20+12=32 and - is 16

2

26

10+16=26 and - is 13

2

48

16

208 area of mid. sect,

4

832

320

120

1272

40

6)50880

8480 folidity in cubic feet.

By RULE II.

12 the longest side of the lesser base.

10 half the longest fide of the greater base.

22

To the breadth of the lesser base.

220 reserved number.

Again,

20 the longest side of the greater base,

6 half the longest side of the lesser bafe.

26

16 breadth of the greater base.

416

416

220

636
40

3)25440

8480 cubic feet as above.

Ex. 2. Required the solid content of a trough, in the form of a prismoid, whose greater base is 24 inches by 30, and lesser 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 5 at the greater base, and 12 inches by to at the lesser, its depth being 4 feet? Ans. 57408 solid inches, or 33.2 feet,

PROBLEM X.

To find the folidity of a wedge

RULE.

Multiply the sum of twice the length of the base, 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 base is equal to that of the edge, the wedge is equal to one half a prism of the fame base and altitude.

EXAMPLE I.

How many folid feet are in a wedge whose base 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?

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Multiply the circumference by the diameter, and the productwill be the furface: Or,

Multiply the square of the diameter by 3.1416 for the furface.

RULE 2. Multiply the square of the axis by.7854, and four times the product will be the fuperficies.

EXAMPLE I.

How many square 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

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