38 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.
 

038-circular-log.gif

 

  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?

13 Review Problem - Volume of water inside the Venturi meter

Problem 13
The accompanying figure represents the longitudinal view of a Venturi meter, a device designed to measure the flow of water in pipes. If the throat of the of the meter is 6 in. long and has an inside diameter of 4 in., find the volume of water in the meter which is used in 12-in. pipe line if the altitudes of the tapering parts are in the ratio 1:3 and the smaller altitude measures 12 in.
 

013-venturi-meter.gif