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. 12634059375 cubic inches.

PROBLEM

PROBLEM XI.

To find the convex surface of a sphere or globe.

RULE.

Multiply its diameter by its circumference.

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

EXAMPLES.

1. Required the convex superficies of a globe, whose diameter or axis is 24 inches.

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 7957 miles, or its circumference 25000 miles?

Ans. 198943750 square miles.

4. The axis of a sphere being 42 inches, what is the convex superficies of the segment, whose height is 9 inches? Ans. 11875248 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.

PROBLEM XII.

To find the solidity of a sphere or globe.

RULE.

Multiply the cube of the axis by 5236.

EXAMPLES.

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

: 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.

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 height is 24, and the diameter of its base 8.61684. Ans. 715695.

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 ?