Mensuration of the Round Bodics.

5. What is the surface of a sphere whose diameter is

14 feet?

Ans. 5,58506 sq. ft.

PROBLEM VIII.

8. To find the convex surface of a spherical zone.

RULE.

Multiply the height of the zone by the circumference of a great circle of the sphere, and the product will be the convex surface.

2. The diameter of a sphere is 12 feet: what will be the surface of a zone whose altitude is 2 feet?

Ans. 78,54 sq. ft.

QUEST.-8. How do you find the convex surface of a spherical zone?

Mensuration of the Round Bodies.

3. The diameter of a sphere is 21 inches: what is the

surface of a zone whose height is 4

inches? Ans. 296,8812 sq. in.

4. The diameter of a sphere is 25 feet, and the height of the zone 4 feet: what is the surface of the zone? Ans. 314,16 sq. ft.

PROBLEM IX.

9. To find the solidity of a sphere.

RULE I.

Multiply the surface by one-third of the radius and the product will be the solidity.

2. The diameter of a sphere is 7957,8: what is its so

lidity?

Ans. 263863122758,4778.

QUEST.-9. How do you find the solidity of a sphere by the first rule ?

Mensuration of the Round Bodies.

3. The diameter of a sphere is 24 yards: what is its solid content?

Ans. 7238,2464 cubic yds.

4. The diameter of a sphere is 8: what is its solidity?

Ans. 268,0832.

RULE II.

10. Cube the diameter and multiply the number thus found, by the decimal,5236 and the product will be the solidity.

EXAMPLES.

1. What is the solidity of a sphere whose diameter is 20?

Ans. 4188,8.

2. What is the solidity of a sphere whose diameter is 6?

Ans. 113,0976.

3. What is the solidity of a sphere whose diameter is 10?

Ans. 523,6.

QUEST.-10. How do you find the solidity of a sphere by the second rule ?

Mensuration of the Round Bodies.

PROBLEM X.

11. To find the solidity of a spherical segment with one base.

RULE.

1st. To three times the square of the radius of the base add the square of the height.

2d.

Multiply this sum by the height, and the product by the decimal,5236: the result will be the solidity of the segment.

EXAMPLES.

1. What is the solidity of the segment ABD, the height BE being 4 feet, and the diameter AD of 4 the base being 14 feet?

First,

(72x3+42)=147+16=163:

Then, 163×4x,5236-341,3872 solid feet, which is the solidity of the segment.

2. What is the solidity of the segment of a sphere, whose height is 4, and the radius of its base 8?

Ans. 435,6352.

QUEST.-11. How do you find the solidity of a spherical segment?

Mensuration of the Spheroid.

3. What is the solidity of a spherical segment, the diameter of its base being 17,23368, and its height 4,5? Ans. 572,5566.

4. What is the solidity of a spherical segment, the diameter of the sphere being 8, and the height of the segment 2 feet?

Ans. 41,888 cubic feet.

5. What is the solidity of a segment, when the diameter of the sphere is 20, and the altitude of the segment 9 feet?

Ans. 1781,2872 cubic feet.

OF THE SPHEROID.

12. A spheroid is a solid, described by the revolution of an ellipse about either of its axes.

be revolved about the shorter axis CD, the solid described is called an oblate spheroid.

QUEST.-12. What is a spheroid? 13. What if an ellipse be revolved about the transverse axis, what is the solid which it describes called? If it be revolved about the conjugate axis, what is the solid called?