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2. Required the content of a rectangular prismoid, whose greater end measures 12 inches by 8, the less end 8 inches by 6, and the perpendicular height 5 feet.

Ans. 2.453 feet.

3. What is the content of a cart or waggon, whose inside dimensions are as follow : at the top, the length and breadth 81 and 55 inches ; at the bottom, the length and breadth 41 and 29 inches; and the height 474 inches ?

Ans. ! 26340.59375 cubic inches.

PROBLEM

PROBLEM XI.

To find the convex surface of a sphere or globe.

RULE.

Multiply its dianieter by its circumference.

NOTE. In like manner, the convex surface of any 2018 or segment is found by multiplying its height by the whole circumference of the sphere.

EXAMPLES,

24

1. Required the convex superficies of a globe, whose diameter or axis is inches.

3'1416

24 diameter.

[graphic]

125664
62832

75'3984 circumference.

24

3015936 1507968

1809'5616 answer.

2. What is the convex surface of a sphere, whose diameter is 7, and circumference 22 ?

Ans. 154.

3. Required the area of the surface of the earth, its diameter, or axis, being 79570 miles, or its circumference 25000 miles ?

Ans. 198943750 square miles. 4. The axis of a sphere being 42 inches, what is the

4 convex superficies of the segment, whose height is 9 inches?

Ans. 1187-5248 inches.

5. Required the convex surface of a spherical zone, whose breadth or height is 2 feet, and cut from a sphere of 12 feet diameter.

Ans. 78.54 feet.

[blocks in formation]

Multiply the cube of the axis by •5236.

EXAMPLES.

1. What is the solidity of the sphere, whose axis is 12 ?

[blocks in formation]

VOL. II.

2. To find the content of the sphere, whose axis, is 2 feet 8 inches.

Ans. 9*9288 feet. 3. Required the solid content of the earth, supposing its circumference to be 25000 miles.

Ans. 263858149120 miles.

PROBLEM XIII.

To find the solidity of a spherical segment.

RULE.

To

3

times the square of the radius of its base add the square of its height; then multiply the sum by the height, and the product by *5236.

EXAMPLES.

1. Required the content of a spherical segment, its height being 4 inches, and the radius of its base 8. 8

А

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832

2. What 2. Required

2. What is the solidity of the segment of a sphere, whose height is 9, and the diameter of its base 20 ?

Ans. 1799-6132. 3. Required the content of the spherical segment, whose keight is 25, and the diameter of its base 8:61684.

Ans. 71-5695

PROBLEM XIV.

To find the solidity of a spherical zone or frustum.

RULE.

Add together the square of the radius of each end and of the square of their distance or the height ; then multiply the sum by the said height, and the product again by

1-5708.

EXAMPLES.

1. What is the solid content of a zone, whose greater diameter is 12 inches, the less 8, and the height 10 ?

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