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PROBLEM XIV.

To find the solidity of a spherical segment.

RULE I.

From the treple prodụct of the diameter of the sphere, multiplied by the square of the segment's height, fubtract twice the cube of the height, and the remainder, multiplied by 5236, will give the solidity.

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

EXAMPLE.

Required the solidity of a spherical segment, whose height is & inches, and the radius of its base 16 inches.

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3485.08.6 solid inches as before. Ex. 2. Required the folidity of a segment, whose base diae meter is 100, and its height 13.5 inches.

Ans: 54302.75235 cubic inches. Ex. 3.

How many folid miles are in either frigid zone, the height being 329 miles, and diameter of its base 3168 miles ?

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 square of the zone's height;

multiply

1

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

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

Rule 3. Add into one sum twice the square of the sphere's diameter, and the square of the diameter of the zone's base ; divide this sum by 3.8197, and multiply the quotient by the zone's height; the product is the soliditý.

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

By RULE I.
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Ex. 2. Required the solidity of a zone, whose greater diameter is 2 feet, the less I foot 4 inches, and the height foot 8 inches.

Ans. 10723.328 inches. Ex. 3. What is the solid content of a zone, whose height is 30, and end diameters 60 and 40 inches?

Anf. 75398.4 cubic inches. Ex. 4. What is the solidity of a zone, whose height is 8 inches, and diameter of the ends 12 inches ?

Anf. 1172 864 cubic inches.

PROBLEM XVI. Fig. 90.

To find the area of a circular spindle.

RULE.

Multiply the length of the spindle by the radius of the revolving arch; again multiply the distance between the centre of the revolving arch and the centre of the spindle Iby the length

of

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