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SECTION XII.

Frustum of a Sphere.

To find the solidity of a frustum of a sphere.

To the squares of the radii of the two bases, add one third the square of the height; this sum multiplied by the height, and the product by 1.5708 gives the solidity.

1. What is the solidity of a frustum of a sphere, the diameters of which are 18 and 22 inches, and perpendicular distance 15 inches?

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2. What is the solidity of a zone or middle frustum of a sphere, the diameters of the bases being 24, and altitude 12 inches!

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3. What is the solidity of the middle frustum of a sphere, the greater diameter 12 inches, less diameter 10 inches, and height 4 inches? ANS. 416.785 cubic in.

4. If the diameters of the bases of a zone are 4 feet and 5 feet, and height 3 feet, what is the solidity?

ANS. 62.1565 cubic feet.

SECTION XIII.

A Spheroid.

A Spheroid is an oblong solid, formed by the revolution of an ellipsis about its transverse or conjugate diam

eter.

If the revolution be on its transverse diameter, the solid is called a prolate spheroid; if the revolution be on its conjugate diameter, the solid is an oblate spheroid.

In a prolate spheroid, the transverse diameter is the axis.

In an oblate spheroid, the conjugate diameter is the axis.

To find the solidity of a Spheroid:

Multiply the square of the revolving diameter by its axis, and the product by .5236 for the solidity.

1. What is the solidity of a prolate spheroid, the diameters of which are 17 and 24?

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A B revolving diameter, C D axis.

17×17=289×24=6936X.5236=3631.689

solidity.

2. What is the solidity of an oblate spheroid, the di

ameters of which are 28 and 16?

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3. What is the solidity of an oblate spheroid, the diameters of which are 8 and 12 inches?

ANS. 6031.87 cubic in.

4. If the axis of a prolate spheroid be 18 inches, and the revolving diameter 12 inches, what is the solidity? ANS. 1357.17 cubic in.

SECTION XIV.

Segment of a Spheroid.

To find the solidity of the Segment of a Spheroid.

From the product of three times the axis, subtract twice the height of the segment; multiply the remainder by the square of the height, and the product by .5236. Then,

as

the square of the axis is to the square of the revolving diameter, so is the last product to the solidity.

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