- - AGRICULTURE CORE CURRICULUM - - (CLF2000) Advanced Core Cluster: AGRICULTURAL MECHANICS (CLF2150) Unit Title: MEASUREMENTS ___________________________________________________________________________ (CLF2155) Topic: SQUARE 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: 25' measuring tape, objects and land to measure Cooper, Elmer L. (1987). AGRICULTURAL MECHANICS: FUNDAMENTALS AND APPLICATIONS. Albany, NY: Delmar Publishers. Evaluation: Quiz by instructor. TOPIC PRESENTATION: SQUARE MEASUREMENTS A. The Definition and Equivalents of Square Measures 1. Square measure is a system for measuring area. a. Area is the amount of surface included within limits. b. Square measurement is different from linear measurement. 6' Perimeter _____________________________ | | | | | | | P = 2 X length + 2 X width |____|____|____|____|____|____| = (2X6) + (2X4) | | | | | | | = 12 + 8 |____|____|____|____|____|____| = 20 feet | | | | | | | 4' |____|____|____|____|____|____| Area | | | | | | | |____|____|____|____|____|____| A = 24 square feet 2. When determining the area of a geometric figure, all linear measurements must be expressed in the same unit of measurement. B. Finding Area of Rectangles and Squares 1. Rectangle Formula a. A = l X w or A = lw a. The formula reads, "The area of a rectangle is equal to the length times the width." Example: Find the area of a rectangular barn that is 85 feet long by 50 feet wide. 50' _________ | | l = 85 | | w = 50 | Barn | A = ? | | 85' | Area | A = 85 X 50 | | A = 4,250 sq ft | | |_________| 2. Square Formula 2 a. A = s b. The formula reads, "The area of a square is equal to the length of its side squared." Example: Find the area of a square feed bin. _____________ | | s = 4 | | A = ? | Feed Bin | 4' 2 | Area | A = 4 | | A = 4 X 4 |_____________| P = 16 sq ft 4' C. Finding the Area of Circles and Cylinders 1. Circle Formula 2 a. A = pi r c. The formula reads, "The area of a circle is equal to pi times the radius squared." Example: Find the area of grain silo floor. Grain Silo Floor . /|\ . r = 9 . | . pi = 3.14 . | . 2 . 18' . A = 3.14 X 9 . | . A = 3.14 (9 X 9) . \|/ . A = 3.14 X 81 A = 254.34 sq ft 2. Cylinder Formulas a. A = Ch or A = pi X d X h or A = 2 X pi X r X h b. The formula reads, "The curved-surface area of a cylinder is equal to the circumference of an end times the height." Example: In order to know how much sheet metal to order for constructing a round ventilation duct, determine the curved-surface area of the cylinder. Ventilation Duct ___ / \ C = 10" or 0.83' |C=10"| h = 8' or 96" |\___/| A = ? | | | | Convert C and h to the same units of measure | | h = 8' | | A = 10 X 96 or A = .83 X 8 | | A = 960 sq in A = 6.6 sq ft | | | | Convert area in sq in to sq ft | | \___/ A = 960 / 144 A = 6.6 sq ft 2 c. A = pi X d X h + 2pi X r d. The formula reads, "The total outside area of a cylinder is equal to the curved-surface area plus the area of the two bases (ends)." E. Finding the Area of Triangles and Trapezoids 1. Triangle Formula a. A = 1/2bh or bh/2 b. The formula reads, "The area of a triangle is equal to one half the base times the height." /|\ / | \ / | \ / |h \ / | \ /__________|__________\ b Example: Determine the amount of siding required to cover a building's gable by finding the area of the triangle. Gable /|\ b = 15 / | \ h = 8 / | \ A = ? / |8' \ / | \ A = 15 X 8 divided by 2 /__________|__________\ | 15' | A = 60 sq ft 2. Trapezoid Formula ________b1________ /| \ / | \ / | h \ / | \ / | \ /_____|______________________\ b2 a. A = h X b1 + b2 divided by 2 b. The formula reads, "The area of a trapezoid is equal to the height times the average of the two parallel sides or bases." Example: To help a farmer know how much fertilizer to order for a trapezoid- shaped field, calculate its area. Field h = 120 150' b1 = 150 __________________ b2 = 200 / | \ A = ? / | \ / | 120' \ A = 120 X 150 + 200/2 / | \ / | \ A = 120 X 350/2 /_____________|______________\ A = 120 X 175 A = 21,000 sq ft 200' Convert sq ft to acres A = 21,000/43,560 A = .48 acre _________________________________________________________ ACTIVITY: 1. Take actual measurement of plots and fields around the school shop or farm and determine individual and total acreage. 2. Determine how much sheet metal was used in constructing a barrel, feed bin, etc. _________________________________________________________ 6/27/91 OLR/tf #%&C