Problem 38
A log 18 ft. long is 2 ft. in diameter at the top end and 3 ft. in diameter at the butt end.
 

1. How many cubic feet of wood does the log contain?
2. How many cubic feet are there in the largest piece of timber of square cross section that can be cut from the log?
3. How many cubic feet are in the largest piece of square timber of the same size throughout its whole length?
4. How many board feet does the piece of timber in (c), a board foot being equivalent to a board 1 ft. square and 1 in. thick?

Hint: In (b) the larger end is the square ABCD. What is the smaller end? In (c) one end is the square EFGH. What is the other end?

A pyramid is a polyhedron with a polygon base of any shape, and all other faces are triangles which have common vertex.
 

A right circular cylinder is a cylinder whose base is a circle and whose elements are perpendicular to its base.
 

There are two very common prisms; the cube and rectangular parallelepiped. In non-mathematical term, both are called box.
 

Solids of Revolution by Integration

The solid generated by rotating a plane area about an axis in its plane is called a solid of revolution. The volume of a solid of revolution may be found by the following procedures: