- -  AGRICULTURE CORE CURRICULUM - - 
 
(CLF2000) Advanced Core Cluster: AGRICULTURAL MECHANICS
 
 (CLF2150) Unit Title: MEASUREMENTS 
 
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 (CLF2156) Topic: CUBIC MEASUREMENTS              Time   Year(s) 
                                                   3 hours  1 / 2 / 3 / 4
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          Topic Objectives: Upon completion of this lesson, the students
                             will be able to:
 
          Learning Outcome #:
 
             (C-1) - Measure objects correctly with a ruler, tape, or
                       framing square.
 
             (C-4) - Differentiate between U.S. Customary and metric
                       measurement units (in linear, area, and volumetric
                       measurements).
 
             (C-6) - Use various methods to determine the mass and volume
                       of regularly and irregularly shaped objects.
 
          Special Material and Equipment: 25' measuring tape, containers to 
                       measure
 
          References: Cooper, E. L. (1987). AGRICULTURAL MECHANICS:
                         FUNDAMENTALS AND APPLICATIONS. Albany, NY: Delmar
                         Publishers.
 
          Evaluation: Quiz by instructor.
 
TOPIC PRESENTATION: CUBIC MEASUREMENTS
 
A. The Definition and Use of Cubic Measure
 
   1. A cubic measure is a system of measurement of volume or capacity of
       an object expressed in cubic units.
 
   2. Cubic measure requires three dimensions:
 
       a. Linear measure adds only one dimension to find total distance.
 
       b. Square measure multiplies two dimensions to find area of a
           surface.

       c. Cubic measure multiplies three dimensions (length, width, and
           height) to find the volume of various types of structures and
           containers.

   3. When determining the volume of an object, all measurements must be
       expressed in the same units of measurement.
B. Finding the Volume of Rectangular Solids and Cubes
 
   1. Rectangular Solids Formula
 
       a. V = l X w X h
 
       b. The formula reads, "The volume of a rectangular solid is equal
           to the length times the width times the height."
 
       Example:
 
       To help a mechanic know how much of an alkaline compound would be
       needed to mix with water, determine the volume of this hot tank.
 
                  Hot Tank      
           ___________________          l = 6
         /                  /|         w = 4
        /___________________/ |         h = 4
        |                  | | 4'      V = ?
        |                  | | 
        |                  | |           V = 6 X 4 X 4
        |                  | /           V = 6 X 16
        |___________________|/ 4'        V = 96 cubic feet
                    
                  6'
 
   2. Cube Formula
                3
       a. V = s
 
       b. The formula reads, "The volume of a cube is equal to its side
           cubed."
 
       Example:
 
       To determine how much feed a feed bin can hold, one must first
       calculate its volume.
 
              Feed Bin      
            __________ 
          /         /|         s = 4
         /__________/ |         V = ?
        |         | | 4'           3 
        |         | |         V = 4 
        |         | |         V = 4 X 4 X 4
        |         | /          V = 4 X 16
        |__________|/ 4'       V = 64 cubic feet
              4'
C. Finding the Volume of Cylinders and Cones
 
   1. Cylinder Formula
                         2
       a. V = pi X r X h
 
       b. The formula reads, "The volume of a cylinder is equal to pi 
           times the radius squared times the height."
 
       Example:
 
       Pier Footing
           ___
          /  \              pi = 3.14
         | C=1'|              r = 0.5
         |\___/|              h = 2.0
         |    |              V =  ?
         |    |                           2
         | ___ | h = 2'       V = 3.14 X .5 X 2
         |/  \|              V = 3.14 X .25 X 2
         |    |              V = 3.14 X .5
          \___/               V = 1.57 cu ft
 
   2. Cone Formula
                               2 
       a. V = 1/3 X pi X r X h
 
       b. The formula reads, "The volume of a cone is equal to 1/3 times
           pi times the radius of the base squared, times the height."
 
       Example:
 
       To determine how much grain can be held in the conical roof portion
       of a large circular grain bin, calculate the volume of the cone.

       Conical Roof of Grain Bin

                /.\                pi = 3.14
              / : \               r = 4
            /   :   \             h = 9
          /     9'    \           V = ?
        /     . : .     \                     2
      / . '   :   '  . \       V = 3.14 X 4 X 9 divided by 3
      . _________8'_________.
       .                 .         V = 3.14 X 16 X 9 divided by 3
         .             .   
           ' . . . '             V = 3.14 X 144 divided by 3

                                     V = 452.16 divided by 3

                                     V = 150.72 cu ft
          _________________________________________________________
         ACTIVITY:
 
         1. Measure various rectangular and cylindrical containers 
             or buildings and determine their volumes. 
 
         2. Measure a paper-cone cup and calculate how much water 
             it can hold.
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