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Unit 2: Engineering Design Process Foundations of Technology 3 Calculating Area and Volume Lesson 5: Prototyping and Modeling

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The Big Idea Big Idea: At various intervals of the Engineering Design Process, conceptual, mathematical and physical models are used to evaluate the design solution.

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Area and Volume Definitions: Area – the amount of space inside a two- dimensional shape. Surface area – the total area of all surfaces on a three-dimensional object. Volume – the amount of space a three- dimensional object occupies.

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Area Square: a = the length of all sides, as all sides are equal Equation for Area (A) = s X s = s² = A s s s s

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Area Rectangle: W = the width of rectangle H = the height of rectangle Equation for Area (A) = W x H = A W H

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Area Triangle: b = the base of the triangle h = the height of the triangle Equation for Area (A) = ½(b x h) = A b h

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Area Circle: r = the radius of the circle Equation for Area (A) = π(r²) = A r

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Practice Questions Calculate the area for the square and rectangle: s = 4 W = 3 H = 2

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Practice Questions Calculate the area for the square and rectangle a = 4 W = 3 H = 2 Area = a² = 4² A = 16 Area = W x H = 3 x 2 A = 6

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Practice Questions Calculate the area for the triangle and circle: b = 4 h = 3 r = 2.5

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Practice Questions Calculate the area for the triangle and circle: b = 4 h = 3 r = 2.5 Area = ½(b x h) = ½(4 x 3) = ½(12) A = 6 Area = π(r²) = π(2.5²) = π(6.25) A = 19.6

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Surface Area Cube: a = the length of all sides, as all six sides are equal Equation Surface Area (SA) = 6(s²) = SA s s s

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Surface Area Rectangular Prism: W = the width of the prism D = the depth of the prism H = the height of the prism Equation Surface Area (SA) = 2(W x H) + 2(D x H) + 2(W x D) = SA W D H

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Surface Area Sphere: r = the radius of the sphere Equation Surface Area (SA) = 4π(r²) = SA r

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Surface Area Cylinder: r = the radius of the cylinder h = the height of the cylinder Equation Surface Area (SA) = 2π(r²) + 2π(r x h) = SA h r

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Practice Question Calculate the surface area for the sphere and cylinder: s = 2 W = 4 D = 2 H = 3

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Practice Question Calculate the surface area for the cube and rectangular prism: Surface Area = 6s² = 6(2²) = 6(4) SA = 24 Surface Area = 2(W x D) + 2(H x D) + 2(W x H) = 2(4 x 2) + 2(3 x 2) + 2(4 x 3) = 2(8) + 2(6) + 2(12) = SA = 52 s = 2 W = 4 D = 2 H = 3

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Practice Question Calculate the surface area for the sphere and cylinder: r = 2 h = 6 r = 1

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Practice Question Calculate the surface area for the sphere and cylinder: r = 2 h = 6 r = 1 Surface Area = 4π(r²) = 4π(2²) = 4π(4) SA = Surface Area = 2π(r²) + 2π(r x h) = 2π(1²) + 2π(1 x 6) = 2π(1) + 2π(6) = SA = 44

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Volume of Cube and Prism Volume of a Cube V = s 3 s s s W D H Volume of a Rectangular prism V = W x H x D

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Volume of Sphere and Cylinder Volume of a Sphere V = 4/3∏(r³) Volume of a Cylinder (V) = ∏(r²)h r h r

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Practice Question Calculate the volume of the cube and rectangular prism: b = 2 W = 4 D = 2 H = 3

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Practice Question Calculate the volume of the cube and rectangular prism: s = 2 W = 4 D = 2 H = 3 Volume = s 3 V = (2 3 ) V = 8 Volume = W x D x H V = 4 x 2 x 3 V = 24

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Practice Question Calculate the volume of the sphere and cylinder: r = 2 h = 6 r = 1.5

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Practice Question Calculate the volume of the sphere and cylinder: r = 2 h = 6 r = 1.5 Volume = 4/3∏(r³) V = (1.33) (3.14) (2 3 ) V = 4.19 x 8 V = Volume = ∏(r²)h V = (3.14) (1.5 2 ) (6) V = (3.14) (2.25) (6) V = 42.39

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