Multiply the circumference of the sphere by its diameter, which will give the whole surface.
Or, square the diameter, and multiply by 3·1416.
Or, square the circumference, and multiply by ·3183;
or divide by 3·1416.
Note.—For the surface of the segment, or frustrum, multiply the whole circumference of the sphere by the height of the part required.
Example.—Required the superficies of a globe whose diameter is 24 inches.
24 × 24 × 3·1416 = 1809·5616 square inches.
To find the solidity of a sphere, or globe.
1. Multiply the surface by the diameter, and take ⅙ of the product.
Or, multiply the square of the diameter by the circumference, and take ⅙ of the product.
2. Cube the diameter, and multiply by ·5236.
3. Cube the circumference, and multiply by ·01688.