038 Review Problem - Circular log with non-uniform cross-section

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?

001 A wire of given density and total mass

Problem 001
A certain wire that weighs 8.5 g/cc has a total mass of 155 kg.

  1. What is the density of the wire in kg/m3?
  2. Find the volume of the wire in cubic centimeter.
  3. If the total length of the wire is 1500 m, find the cross-sectional area in square millimeters.


The Pyramid

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



The Right Circular Cylinder

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

Common Prisms: Cube and Rectangular Parallelepiped

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

Volumes of Solids of Revolution | Applications of Integration

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:

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