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Area and Volume

Area and Volume. Slide Presentation By Mr. Michael Braverman Trenton Public Schools March 2015. Area: The number of UNIT SQUARES it takes to completely cover an object without gaps or overlap. Area is ALWAYS given in SQUARE units (or units 2 )

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Area and Volume

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  1. Area and Volume Slide Presentation By Mr. Michael Braverman Trenton Public Schools March 2015

  2. Area: • The number of UNIT SQUARES it takes to completely cover an object without gaps or overlap. • Area is ALWAYS given in SQUARE units (or units2) • All area FORMULAS are based on the formula of a rectangle (Area = base x height) – see AREA slide show for more. Area and Volume Definitions 1 foot 1 ft2 1 foot

  3. All area FORMULAS are based on the formula of a rectangle (Area = base x height) Area and Volume 3 feet 15 feet2 1 foot 5 feet 1 ft2 1 foot

  4. 1 unit • Volume: • The number of unit CUBES it takes • to completely FILL an object. 1 unit Area and Volume 1 unit Definitions 3 Units 3 Units 5 Units

  5. 1 unit 1 unit Area and Volume • Volume: • The number of unit CUBES it takes to completely FILL an object. 1 unit Definitions • is ALWAYS given in CUBIC units (which are either units of volume or units3)

  6. Volume: • The number of unit CUBES it takes to completely FILL an object. • Volume is ALWAYS given in CUBIC units (which are either units of volume or units3) Area and Volume • All volume FORMULAS where there are two parallel and congruent bases are: • V=Area of the base * height of the solid. • V=Abase * height Definitions

  7. V = Abase * height Area and Volume 5 feet 15 ft2 3 feet 1 foot 1 ft2 1 foot

  8. The Volume of one “unit-slice” (a one-unit thick slice parallel to the base) is equivalent to the area in number, but has cubic units. Area and Volume V = Abase * height 5 feet 15 ft3 3 feet 1 foot 1 foot 1 foot 1 ft3 1 foot

  9. All area FORMULAS are based on the formula of a rectangle (Area = base x height) Area and Volume V = Abase * height 5 feet 15 ft3 3 feet 1 foot 1 foot 1 foot 1 ft3 1 foot

  10. V = Abase * height = 15 ft2 x 1 ft = 15 ft3 Area and Volume 5 feet 15 ft3 3 feet 1 foot 1 foot 1 foot 1 ft3 1 foot

  11. V = Abase * height = 15 ft2 x 2 ft = 30 ft3 V = Abase * height = 15 ft2 x 1 ft = 15 ft3 Area and Volume 5 feet 15 ft3 15 ft3 3 feet 1 foot 1 foot 1 foot 1 ft3 1 foot

  12. V = Abase * height = 15 ft2 x 2 ft = 30 ft3 V = Abase * height = 15 ft2 x 3 ft = 45 ft3 Area and Volume 5 feet 15 ft3 15 ft3 15 ft3 3 feet 1 foot 1 foot 1 ft3 1 foot

  13. V = Abase * height Area and Volume 10 m 6 m 3 m

  14. V = Abase * height BASE  Area and Volume 6 m 3 m AΔ = bh ÷ 2 AΔ = 3m x 6m ÷ 2 AΔ = 18m2 ÷ 2 AΔ = 9m2 10 m 6 m 3 m 9m2

  15. V = Abase * height 9m3 V = 9m2 x 10 m BASE  9m2 9m3 Area and Volume V = 90 m3 6 m 9m3 9m3 9m3 9m3 9m3 9m3 9m3 9m3 9m3 9m3 9m3 9m3 3 m 9m3 per “slice” X 10 slices =90 m3 9m2 9m3 9m3 10 m 9m3 9m3 6 m 3 m 9m3 + 9m3

  16. Sample Problem: Find the volume of a cylinder with a diameter of 3 inches and a height of 5 inches Area and Volume

  17. V = Abase * height Abase Sample Problem: Find the volume of a cylinder with a diameter of 3 inches and a height of 5 inches Area and Volume 3 in 3 in Radius = 1.5in Diameter = 3 in 5 in Circumference = 3 π in Area = 2.25 π in2

  18. V = Abase * height V = 2.25 π in2 * height Area and Volume V = 2.25 π in2 * 5 in V = 11.25 π in3 3 in 3 in Radius = 1.5in Diameter = 3 in 5 in Circumference = 3 π in 5 in Area = 2.25 π in2

  19. Area and Volume 2.25 π in2 3 in The area of the base is 2.25 π in2. The volume of a disc one inch thick is 2.25 π in3. 2.25 π in3 2.25 π in3 2.25 π in3 2.25 π in3 2.25 π in3 V = 2.25 π in3 x 5 V = 11.25 π in3 5 in

  20. Find the volume of a cylinder with a diameter of 3 inches and a height of 5 inches Area and Volume By “Slices”: Abase = 2.25 π in2 V slice = 2.25 π in3 3 in By Formula: V = Abase * height 5 in V = 2.25 π in2 * 5 in V = 11.25 π in3 V cylinder= 2.25 π in3 * 5 V = 11.25 π in3

  21. All volume FORMULAS where there is ONE base and triangular sides that come to a single point (like in a pyramid or cone): • V = Area of the base * height of the solid • 3 • V = Abase * height • 3 Area and Volume Definitions

  22. Try these: Find the volume of: a) b) c) 8 cm 6 cm 6 cm 18 cm 5 cm 8 cm 12 cm 6 cm 15 cm

  23. Try these: Find the volume of: a) b) c) 8 cm 6 cm 6 cm 18 cm 5 cm 8 cm 12 cm 6 cm 15 cm a) 240 cm3 c) 288 cm3 b) 648 π cm3

  24. Try these: Find the volume of: d) e) 6 cm 5 cm 18 cm 8 cm 6 cm • V = Abase * height • 3

  25. Try these: Find the volume of: d) e) 6 cm 18 cm 5 cm 8 cm 6 cm d) 80 cm3 e) 216 π cm3

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