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By RULE II.

50

50

2500

3.1416

15708000
62832

7854.0000 furface.
50

6)392700

65450 Anf.

By RULE III.

50

50

2500

.7854

3927000

15708

1963.5000

50

98175.0000 folid cylin,

2

3)196350

65450 Anf. as above.

Ex. 2. Required the folidity of a fphere of 10 inches diame

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Ex. 4. What is the folidity of a sphere, whose diameter is 3 feet 1 inch?

I

Anf. 15.3483 cubic feet.

Ex. 5. Required the solidity of a globe, its diameter being 8 feet 4 inches. Anf. 303.0092. Ex. 6. How many folid miles are in the terraqueous globe, its diameter being 7958 miles? Anf. 263883017937.1232.

PROBLEM XIII.

To find the furface of any zone, or fegment of a sphere.

RULE.

Multiply the circumference of a great circle of the sphere by the fegment's height, and the product will be the fuperficies.

EXAMPLE I.

Required the fuperficies of a zone, whose height is 3 inches, the diameter of the fphere being 12 inches.

3.1416

12

37.6992 circumference.
3 the zone's height.

113.0976 Anf. in fquare inches.

Ex. 2. Required the surface of a figment of a fphere, whofe height is 1 foot 9 inches, the diameter being 5 feet.

Anf. 27.489 fq. feet. Ex. 3. How many fquare inches will cover a fegraent, whofe height is 1 inch, the diameter of the sphere being 3 inches?

Anf. 9.4248 fq. inches.

PROBLEM

PROBLEM XIV.

To find the folidity of a spherical fegment.

RULE I.

From the treple product of the diameter of the sphere, multiplied by the square of the fegment's height, fubtract twice the cube of the height, and the remainder, multiplied by .5236, will give the folidity.

RULE 2. To thrice the square of the radius of the fegment's base, add the square of its height; then multiply the fum by its height, and the product again by .5236, the last product, is the folidity.

EXAMPLE.

Required the folidity of a spherical segment, whose height is 8 inches, and the radius of its bafe 16 inches..

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3485.08.6 folid inches as before.

Ex. 2. Required the folidity of a fegment, whofe base diameter is 100, and its height 13.5 inches.

Anf. 54302.75235 cubic inches. folid miles are in either frigid zone, the height being 329 miles, and diameter of its bafe 3168 miles?

Ex. 3. How many

Anf. 1315766512 folid miles.

PROBLEM XV.

To find the folidity of the middle zone of a sphere.

RULE I.

When the ends are unequal, add into one fum the squares of the radii of both ends, and the fquare of the zone's height;

multiply

197

multiply the fum by the height, and the product again by 1.5708 for the folidity.

RULE 2. From the folidity of the whole sphere, fubtract the folidity of the fegments ABC and DEF; the remainder is the folidity of the zone.

RULE 3. Add into one fum twice the square of the sphere's diameter, and the fquare of the diameter of the zone's bafe; divide this fum by 3.8197, and multiply the quotient by the zone's height; the product is the folidity.

EXAMPLE I.

Required the folidity of the middle zone of a sphere, whose diameter is 80 inches; the diameter of the zone's base being 48, and height 64 inches.

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