Foundations of Technology Calculating Area and Volume Teacher

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Foundations of Technology Calculating Area and Volume Teacher Resource – Unit 2 Lesson 5

Foundations of Technology Calculating Area and Volume Teacher Resource – Unit 2 Lesson 5 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

The BIG Idea Big Idea: At various intervals of the Engineering Design Process, conceptual,

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. © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Area and Volume Definitions: Area – the amount of space inside a twodimensional shape.

Area and Volume Definitions: Area – the amount of space inside a twodimensional shape. Surface area – the total area of all surfaces on a three-dimensional object. Volume – the amount of space a threedimensional object occupies. © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Area Square: a = the length of all sides, as all sides are equal

Area Square: a = the length of all sides, as all sides are equal a Equation for Area (A) = a² a a a © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Area Rectangle: W = the width of rectangle H = the height of rectangle

Area Rectangle: W = the width of rectangle H = the height of rectangle Equation for Area (A) = W Wx. H H © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Area Triangle: b = the base of the triangle h = the height of

Area Triangle: b = the base of the triangle h = the height of the triangle Equation for Area (A) = h ½(b x h) b © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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

Area Circle: r = the radius of the circle Equation for Area (A) = π(r²) © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology r

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

Practice Questions Calculate the area for the square and rectangle: a=4 W=3 H=2 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Practice Questions Calculate the area for the square and rectangle: a=4 W=3 Area =

Practice Questions Calculate the area for the square and rectangle: a=4 W=3 Area = a² = 4² A = 16 Area = W x H =3 x 2 A=6 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology H=2

Practice Questions Calculate the area for the triangle and circle: h=3 b=4 © 2013

Practice Questions Calculate the area for the triangle and circle: h=3 b=4 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology r = 2. 5

Practice Questions Calculate the area for the triangle and circle: h=3 Area = ½(b

Practice Questions Calculate the area for the triangle and circle: h=3 Area = ½(b x h) = ½(4 x 3) = ½(12) A=6 b=4 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology r = 2. 5 Area = π(r²) = π(2. 5²) = π(6. 25) A = 19. 6

Surface Area Cube: a = the length of all sides, as all six sides

Surface Area Cube: a = the length of all sides, as all six sides are equal Equation Surface Area (SA) = a 6(a²) a a © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Surface Area Rectangular Prism: W = the width of the prism H D =

Surface Area Rectangular Prism: W = the width of the prism H D = the depth of the prism H = the height of the prism Equation Surface Area (SA) = D W 2(W x H) + 2(D x H) + 2(W x D) © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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

Surface Area Sphere: r = the radius of the sphere Equation Surface Area (SA) = 4π(r²) © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology r

Surface Area Cylinder: r = the radius of the cylinder h = the height

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) © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology h r

Practice Questions Calculate the surface area for the cube and rectangular prism: H=3 a=2

Practice Questions Calculate the surface area for the cube and rectangular prism: H=3 a=2 D=2 W=4 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Practice Questions Calculate the surface area for the cube and rectangular prism: H=3 a=2

Practice Questions Calculate the surface area for the cube and rectangular prism: H=3 a=2 D=2 W=4 Surface Area = 6 a² = 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) = 16 + 12 + 24 SA = 52 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

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

Practice Questions Calculate the surface area for the sphere and cylinder: r=2 h=6 r=1 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Practice Questions Calculate the surface area for the sphere and cylinder: Surface Area =

Practice Questions Calculate the surface area for the sphere and cylinder: Surface Area = 2π(r²) + 2π(r x h) r=2 Surface Area = 4π(r²) = 4π(2²) = 4π(4) SA = 50. 24 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology h=6 r=1 = 2π(1²) + 2π(1 x 6) = 2π(1) + 2π(6) = 6. 3 + 37. 7 SA = 44

Volume of Cubes & Prisms Volume of a Cube V= a 3 a Volume

Volume of Cubes & Prisms Volume of a Cube V= a 3 a Volume of a Rectangular prism V=Wx. Hx. D H a a D W © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Volume of Spheres & Cylinders Volume of a Sphere V = 4/3∏(r³) Volume of

Volume of Spheres & Cylinders Volume of a Sphere V = 4/3∏(r³) Volume of a Cylinder (V) = ∏(r²)h r © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Practice Questions Calculate the volume of the cube and rectangular prism: H=3 a=2 D=2

Practice Questions Calculate the volume of the cube and rectangular prism: H=3 a=2 D=2 W=4 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Practice Questions Calculate the volume of the cube and rectangular prism: H=3 a=2 D=2

Practice Questions Calculate the volume of the cube and rectangular prism: H=3 a=2 D=2 W=4 Volume = a 3 V = (23) V=8 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology Volume = W x D x H V=4 x 2 x 3 V = 24

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

Practice Questions Calculate the volume of the sphere and cylinder: r=2 h=6 r = 1. 5 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology

Practice Questions Calculate the volume of the sphere and cylinder: r=2 Volume = 4/3∏(r³)

Practice Questions Calculate the volume of the sphere and cylinder: r=2 Volume = 4/3∏(r³) V = (1. 33) (3. 14) (23) V = 4. 19 x 8 V = 33. 49 © 2013 International Technology and Engineering Educators Association, STEM Center for Teaching and Learning™ Foundations of Technology h=6 r = 1. 5 Volume = ∏(r²)h V = (3. 14) (1. 52) (6) V = (3. 14) (2. 25) (6) V = 42. 39