1. The fixed leg is called the axis of the conè.

12. A sphere, or globe, is described by the revolution of a femicircle about its diameter; the centre and diameter of the sphere are the fame as thofe of the revolving femicircle. Fig. 91.

13. A fegment of any solid is a part cut off the top by a plane parallel to the base. The fruftum of a folid is that part which remains after the fegment is cut off. Fig. 92.

14. The prifmoid is a folid resembling the fruftum of a pyramid, having parallel bafes, and these bases both rectangles, but difproportional. Fig. 93.

15. A zone is that part of a sphere between two parallel planes. Fig. 94.

PROBLEM I. Fig. 85.

To find the fuperficies of a cube

RULE.

Multiply the area of one of its fides by 6, and the product will be the area of the cube.

EXAMPLE I.

Required the fuperficies of a cube, whofe fide is 14 inches.

14

14

56

14

196 area of one of the fides.

6

1176 Anf.

Ex. 2. How many square yards are in the fuperficies of a

cube, whofe fide is 5; fect?

Anf. 20 fq. yds. 1 feeo.

Ex. 3.

How many square feet are in the fuperficies of à cube, whofe fide is 18 inches?

Anf. 13 fq. feet.

PROBLEM II.

To find the folidity of a cube.

RULE.

Multiply the length, breadth, and thickness continually, and the product is the folidity.

EXAMPLE I.

What is the folidity of a cube, whofe fide is 8 feet?

8

8

64

8

Anf. 512 folid feet.

Ex. 2. Required the folidity of a cube, the fide being 15 feet

Ex.

Anf. 3375 feet. 3. Required the folidity of a cube, whose fide is 34 yards. Anf. 34-328125 cub. yds. Ex. 4. How many yards digging are in a cubical cellar 12 feet deep? Ex. 5. How many folid yards are in a cubical cellar, whofe fide is 10 feet?

Anf. 64 cub. yds.

Anf. 372, crib. yds..

PROBLEM III.

To find the fuperficies of a parallelopipedon, or prifin, and of the cylinder.

RULE.

Multiply the perimeter of the end by the length; to the product add twice the area of the end, and the fum will be the fuperficies.

EXAMPLE I.

Required the fuperficies of a parallelopipedon, whofe length is 72 feet, breadth 3 feet, and thickness 2 feet.

Ex. 2. Required the furface of a parallelopipedon, whose length is 72 feet, breadth 5, and depth 4 feet.

Anf 1336 fq. feet.

Ex. 3. What is the fuperficies of a parallelopipedon, whofe length is 15, breadth 6, and thickness 4 inches?

Anf. 2 feet 5 inches.

Ex. 4. Required the furface of a triangular prifin, whose length is 10 feet, and fides 3, 4, 5 feet. Anf. 132 feet.

Ex. 5. Required the fuperficies of a prifm, when the length is 32 feet, and the end a pentagon, whofe fide is 6 feet.

Anf. 1150.037

Ex. 6. What is the superficies of a hexagonal prism, the side. being 10 inches, and the length 20 feet?

Anf. 103.6084375 Sq. feet.

. Ex. 7. Required the convex* furface of a cylinder, whofe diameter is 10 inches, and length 141 feet.

Anf. 37.961 fq. feet. Ex. 8. Required the fuperficies of a cylinder, whose length is 20 feet, and diameter of its end 5 feet.

Anf. 378.660975 fq. fɛçt•

PROBLEM IV.

To find the folidity of a parallelopipedon, a prism, or of a cylinder

RULE.

Multiply the area of the end by the length, and the product will be the folidity.

EXAMPLE I.

Required the folidity of a parallelopipedon, whofe length is 20 feet, breadth 18 inches, and thickness 8 inches.

When the convex furface is required, the area of both ends is omitted

Ex. 2. Required the folidity of a parallelopipedon, whose length is 45 feet, breadth 10 feet, and depth 5 feet.

Anf. 2475 cubic feet.

Ex. 3. Required the folidity of a parallelopipedon, whose three dimensions are 30, 44, and 2 feet.

Anf. 289 folid feet. Ex. 4. What is the folid content of a parallelopipedon, whose length is 25, breadth 3, and thickness 2 feet? Anf. 150.

Ex. 5. Required the folidity of a triangular prifm, whofe length is 10 feet, one side of its triangular base being 14 inches, and the p.rpendicular falling upon it from the oppofite angle, 10 inches. Anf. 5 feet, 1 inch 3 parts.

Ex. 6. Required the folid content of a pentagonal prism, whose length is 20 feet, and fide 10 feet. Anf. 3440.95 feet. Ex. 7. The fame dimensions being given, required the folidity of an octagonal prifm. Anf. 9656.854 cubic feet. Ex. 8. On the fame fuppofition, required the folidity of a decagonal prism. Anf. 15388.41 folid feet. Note, From the foregoing examples it is evident, that the nearer the figure of the base approaches to a circle, the greater will the folidity be.