6. The diameter of a sphere is 18 inches; the surface is divided into three parts by parallel planes which divide the diameter in the ratio of 1, 2, 3; find the area of the portion intercepted between the planes.

Ans. 339 inches.

7. Find the curve surface of the segment of a sphere whose radius is 54 yards, and depth 31 yards.

Ans. 57 yards.

XXXVII.

21.

To find the solidity of a sphere.

Multiply the cube of the diameter by 11 and divide by

Ex. Find the solidity of a sphere whose diameter is Io ft. 6 in.

XXXVIII.

To find the solidity of the segment of a sphere.

(1) When the diameter of the sphere and the height of the segment are given: From three times the diameter subtract twice the height of the segment; multiply the difference twice by the height of the segment; then multiply by 11 and divide by 21.

Ex. The diameter of a sphere is 7 ft. 3 in.; find the solidity of a segment whose height is 3 ft. 6 in.

(2) When the dimensions of the segment are given: To three times the square of the radius of the base add the square of the depth; multiply the sum by the depth; then multiply by 11 and divide by 21.

T. M.

6

Ex. Find the solidity of a segment of a sphere whose depth is 6 inches, and radius of the base 15 inches.

152 × 3 =675
62 = 36

711

6

4266

4266

3 46926

7 15642

22344 Ans.

XXXIX.

To find the solidity of a spherical shell.

Multiply the difference of the cubes of the inner and outer diameters by 11, and divide by 21.

Ex. Find the weight of a spherical shell of cast iron whose inner and outer diameters are 16 and 18 inches.

XL.

Given the solidity of a sphere to find the diameter. Multiply the solidity by 21, and divide by 11; then extract the cube root.

Ex. Find the diameter of a sphere whose solidity is 63457.

I. Find the solidity of a sphere whose diameter is

9 inches.

Ans. 449'101.

2. Find the weight of a spherical shot whose diameter is 8 inches.

Ans. 67 lbs.

3. Find the solidity of the segment of a sphere whose diameter is 18 inches, and height 5 inches.

4.

Ans. 681*345.

Find the number of gallons contained in a spherical boiler the diameter of whose brim is 4 feet, and depth 2 ft. 6 in. Ans. 149.

5. Find the solidity of a segment of a sphere the diameter of whose base is 6 ft. 10 in., and height 3 ft. 6 in. Ans. 86-663 feet.

6. Find the diameter of a sphere whose solidity is 5946 cubic inches. Ans. 22.474.

Find the diameter of a sphere which contains one cubic yard. Ans. 3721 feet. 8. Find the solidity of a spherical shell whose inner and outer diameters are 12 and 15 inches. Ans. 862.

9. Find the weight of a spherical shell of cast iron whose inner and outer diameters are 8 and 10 inches.

Ans. 63 lbs.

10. The diameter of a sphere is 27 inches, and the sphere is divided into three parts by two parallel planes which divide the diameter in the ratio of 2, 3, 4; find the content of each part. Ans. 1301, 42993, 47094.

THE SPHEROID.

If an ellipse revolve about the transverse diameter it will generate a solid called the prolate spheroid; if it revolve about the conjugate diameter, the spheroid is oblate.

XLI.

To find the solidity of a prolate spheroid.

Multiply the square of the conjugate by the transverse diameter; then multiply by 11, and divide by 21.