# Volume

## 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.

- How many cubic feet of wood does the log contain?
- How many cubic feet are there in the largest piece of timber of square cross section that can be cut from the log?
- How many cubic feet are in the largest piece of square timber of the same size throughout its whole length?
- 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

## 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: