- - AGRICULTURE CORE CURRICULUM - - (CLF2000) Advanced Core Cluster: AGRICULTURAL MECHANICS (CLF2150) Unit Title: MEASUREMENTS ___________________________________________________________________________ (CLF2154) Topic: LINEAR MEASUREMENTS Time Year(s) 3 hours 1 / 2 / 3 / 4 ___________________________________________________________________________ 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: Twelve-inch ruler divided to the 16th of an inch which also contains a metric scale References: Cooper, Elmer L. (1987). AGRICULTURAL MECHANICS: FUNDAMENTALS AND APPLICATIONS. Albany, NY: Delmar Publishers. Evaluation: Quiz by instructor. TOPIC PRESENTATION: LINEAR MEASUREMENTS A. The Definition and Use of Linear Measure 1. Linear a. The adjective actually comes from the word line. b. It means "of a line or lines." 2. Linear Measure a. This term refers to the measurement of lines. 1) A line is the distance between two points. 2) It is one-dimensional (having length but no width or thickness). b. The lines to be measured can be curved, irregular, or straight. B. Finding "Perimeters 1. Definition of "perimeter" a. This word means the distance around the outside of an area or an object. b. For example, the legal boundaries of a ranch form its perimeter. 2. The Rectangle a. The rectangle is a four-sided plane figure with four right angles (90 degrees). 1) The adjective, plane, in the definition describes the figure as two dimensional (having length and width but no thickness). 2) All four sides are not equal. l (length) ________________________________ | | | | | | w | RECTANGLE | w (width) | | | | |________________________________| l b. In finding the perimeter of a rectangle, there is a long and a short method. 1) Using the long method, you would add all the sides: l + w + l + w 2) The easier short method employs a formula: p = 2 X length + 2 X width a) This formula reads, "The perimeter of a rectangle equals two times the length plus two times the width." b) A formula uses letters to stand for different measurements, so you only have to replace the letters with numbers to solve a particular problem. Example: To determine how many feet of wire are needed to fence a rectangular pasture 150' long by 85' wide, use the formula to find the perimeter. _____________ | | l = 150 | | w = 85 | | p = ? | | | | | Pasture | 150' length | | | | p = 2 X length + 2 X width | | p = (2 X 150) + (2 X 85) | | p = 300 + 170 |_____________| p = 470 feet 85' width 3. The Square a. A square is a plane figure with four equal sides and four right angles. b. The formula for finding the perimeter of a square is P = 4s. 1) The letter "s" stand for the length of the sides. 2) The formula reads, "The perimeter of a square equals four times the length of its sides. Example: To determine the linear feet of 2" X 4" lumber required for concrete forms for a hog pen floor whose sides are 16,' find its perimeter. _____________ | | s = 16 | | p = ? | Hog Pen | 16' | Floor | p = 4s | | p = 4 X 16 |_____________| P = 64 feet 16' C. Finding the Circumference of Circles 1. Definitions a. A circle is closed plane curve every point of which is equally distant from a point within it. b. The circumference is the perimeter (distance) around a circle. c. The diameter is the distance across a circle, through the center. d. The radius is half of the diameter (from the center to the circle line. . /|\ . . /|\ . . | . . | . . | . . | . . d . C . r . C . | . . . . \|/ . . _ . 2. Formulas a. The formulas used for finding a circumference, diameter, and radius are derived from the relationship that exists between any circle's circumference and diameter. 1) This relationship is referred to as the RATIO of the circumference to the diameter. circumference/diameter = 3.14 (rounded off) 2) This ratio of circumference to diameter is equal to 3.14 (rounded off). a. The number 3.14 has been named with the Greek letter pi. b. Various formulas have been worked out from the ratio, c/d = pi. b. To find a circle's circumference, either of two formulas can be used: 1) C = pi X diameter 2) C = 2X pi X radius Example: Find the circumference of a grain silo when the diameter is 25.' . /|\ . d = 25 . | . pi = 3.14 . | . C = ? . 25' . ? . | . C = pi X diameter . \|/ . C = 3.14 x 25 C = 78.5 feet c. To find a circle's diameter, either of two formulas can be used: 1) d = C/pi 2) d = 2r Example: Find the diameter of a stock tank when the circumference is 30'. . /|\ . C = 30 . | . pi = 3.14 . | . d = ? . ? . 30' . | . d = C/pi . \|/ . d = 30/3.14 d = 9.55 feet d. To find a circle's radius, either of two formulas can be used: 1) r = d/2 2) r = C/pi _________________________________________________________ ACTIVITY: 1. Measure the length and width of both rectangular and square plots and determine their perimeters. 2. Calculate the diameter and circumference of various round objects in the shop. _________________________________________________________ 6/27/90 OLR/tf #%&C