24. How is the mean proportional found for the above?
By multiplying the areas of the two ends together and extracting the square root of their product. A more simple rule is the following: As the diameter of the large end is to that of the small end, so is area of base to mean proportional required.
25. How is the content of a spherical segment found?
From three times the diameter of the sphere, take double the height of the segment, then multiply the remainder by the square of the height, and this product by .5236; or, to three times the square of the radius of the segment’s base, add the square of its height, then multiply the sum by the height, and this product by .5236, for the content.
26. How is the capacity or content of a Gomer chamber computed?
This chamber being the frustum of a cone with a hemispherical bottom, its capacity will be found by applying the foregoing rules, viz: first find the content of the frustum, then that of the spherical segment or bottom, and add their contents into one sum for the capacity.
27. How is the content of a rectangular box ascertained?
Multiply the length by the breadth, and this product by the depth.
28. How is the capacity of a cylinder calculated?
Multiply the area of the base by the height.