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

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

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

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

V=Area of the base * height of the solid. Area and Volume Definitions 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) All volume FORMULAS where there are two parallel and congruent bases are: V=Area of the base * height of the solid. V=Abase * height

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

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

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

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

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

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

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

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

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

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

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

Area and Volume Radius = 1.5in Diameter = 3 in Circumference = 3 π in V = Abase * height V = 2.25 π in2 * height 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

The area of the base is 2.25 π in2. Area and Volume 2.25 π in2 2.25 π in3 2.25 π in3 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 V = 2.25 π in3 x 5 V = 11.25 π in3 2.25 π in3 2.25 π in3 5 in

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

V = Area of the base * height of the solid Area and Volume Definitions 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

Try these: 8 cm 6 cm 6 cm 18 cm 5 cm 8 cm 12 cm 6 cm 15 cm 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

Try these: 8 cm 6 cm 6 cm 18 cm 5 cm 8 cm 12 cm 6 cm 15 cm a) 240 cm3 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

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

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