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Measurement- Area and Volume

Measurement- Area and Volume. Agriculture Mechanics I. Calculating Area. Square measure is a system for measuring area. The area of an object is the amount of surface contained within defined limits. The area of a square or rectangle is equal to the length times the width or; A = l x w

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Measurement- Area and Volume

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  1. Measurement- Area and Volume Agriculture Mechanics I

  2. Calculating Area • Square measure is a system for measuring area. The area of an object is the amount of surface contained within defined limits. • The area of a square or rectangle is equal to the length times the width or; • A = l x w • For example the square below is four square inches. A = l x w A = 2 x 2 A = 4 in² 1 in² 2” 2”

  3. Calculating Area cont. • The area of a circle is equal to pi times the radius squared. • A = π x r² • For example, a circular grain silo has a round floor 18 feet in diameter. What is the area of the circle? d = 18’ r = 9’ π = 3.14 A = π x r² A = 3.14 x (9 x 9) A = 254.34 ft.² 18’

  4. Calculating Area cont. • The area of a triangle is equal to one half the base (b) times the height (h). • A = ½ (b x h) • Example: What is the area of a triangle with a base of 2 yards and a height of 3 yards. b = 2 h = 3 A = ? A = ½ (b x h) A = ½ (2 x 3) A = 3 yds² 3 2

  5. Calculating Volume • A cubic measure is a system of measurement of volume or capacity of an object expressed in cubic units. • Linear measure adds only one dimension to find total distance. • Square measure multiplies two dimensions to find area of a surface. • Cubic measure multiplies three dimensions (length, width and height) to find the volume of structures. • When determining volume of an object, all measurements must be expressed in the same units of measurement.

  6. Calculating Volume cont. • The volume of a rectangular solid is equal to the length (l) times the width (w) times the height (h). • V = l x w x h • Example: Determine the volume of the rectangular crate pictured below. V = l x w x h V = 6 x 4 x 4 V = 96 ft³ 4’ 4’ 6’

  7. Calculating Volume cont. • The volume of a triangular prism is equal to the area of the triangle times the length of the prism. • V = ( ½ (b x h)) x l • The volume of a cylinder is equal to the area of the circular base times the height of the cylinder. • V = ( π x r²) x h

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