Prismatoid

The Prismatoid and the Prismoidal Formula

The General Prismatoid

A general prismatoid is a solid such that the area of any section, say Ay, parallel to and distant y from a fixed plane can be expressed as a polynomial of y of degree not higher than the third.
 

general-prismatoid.jpg

 

A solid is a general prismatoid if

$A_y = a + b_y + cy^2 + dy^3$

Where a, b, c, and d are arbitrary constants which may be positive, negative, or zero.
 

010 Review Problem - Volume of a stick

Problem 10
How many cubic inches of lumber does a stick contain if it is 4 in. by 4 in. at one end, 2 in. by 2 in. at the other end, and 16 ft. long?
 

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