Calculating Area and Volume Foundations of Technology Calculating Area and Volume © 2013...

Foundations of Technology

Calculating Area and VolumeCalculating Area and Volume

© 2013 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology

Teacher Resource – Unit 2 Lesson 5

The BIG IdeaThe BIG Idea

Big Idea:

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


Area and VolumeArea 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.


AreaArea

Square:

a = the length of all sides, as all sides are equal

Equation for Area (A) =

a²


a

a

a

a

AreaArea

Rectangle:

W = the width of rectangle

H = the height of rectangle


W x H


W

H

AreaArea

Triangle:

b = the base of the triangle

h = the height of the triangle


½(b x h)


b

h

AreaArea

Circle:

r = the radius of the circle


π(r²)


r

Practice QuestionsPractice Questions

Calculate the area for the square and rectangle:


a = 4 W = 3

H = 2


Calculate the area for the square and rectangle:


a = 4 W = 3

H = 2

Area = a²= 4²A = 16

Area = W x H= 3 x 2A = 6


Calculate the area for the triangle and circle:


b = 4

h = 3 r = 2.5


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

Cube:

a = the length of all sides, as all six sides are equal

Equation Surface Area (SA) =

6(a²)

Surface AreaSurface Area


a

a

a


Rectangular Prism:

W = the width of the prism

D = the depth of the prism

H = the height of the prism


2(W x H) + 2(D x H) + 2(W x D)


W

D

H


Sphere:

r = the radius of the sphere


4π(r²)


r


Cylinder:

r = the radius of the cylinder

h = the height of the cylinder


2π(r²) + 2π(r x h)


h

r


Calculate the surface area for the cube and rectangular prism:


a = 2

W = 4

D = 2

H = 3


Calculate the surface area for the cube and rectangular prism:


a = 2

W = 4

D = 2

H = 3

Surface Area = 6a²= 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 + 24SA = 52


Calculate the surface area for the sphere and cylinder:


r = 2h = 6

r = 1


Calculate the surface area for the sphere and cylinder:


r = 2h = 6

r = 1Surface Area = 4π(r²) = 4π(2²)= 4π(4)SA = 50.24

Surface Area = 2π(r²) + 2π(r x h) = 2π(1²) + 2π(1 x 6) = 2π(1) + 2π(6) = 6.3 + 37.7SA = 44

Volume of Cubes & PrismsVolume of Cubes & Prisms

Volume of a Cube

V = a3


a

a

a

W

D

H

Volume of a Rectangular prism

V = W x H x D

Volume of SpheresVolume of Spheres & Cylinders & Cylinders

Volume of a Sphere

V = 4/3∏(r³)


Volume of a Cylinder

(V) = ∏(r²)h

r

h

r


Calculate the volume of the cube and rectangular prism:


a = 2

W = 4

D = 2

H = 3


Calculate the volume of the cube and rectangular prism:


a = 2

W = 4

D = 2

H = 3

Volume = a3

V = (23)V = 8

Volume = W x D x HV = 4 x 2 x 3V = 24


Calculate the volume of the sphere and cylinder:


r = 2h = 6

r = 1.5


Calculate the volume of the sphere and cylinder:


r = 2h = 6

r = 1.5Volume = 4/3∏(r³)V = (1.33) (3.14) (23)V = 4.19 x 8V = 33.49

Volume = ∏(r²)hV = (3.14) (1.52) (6)V = (3.14) (2.25) (6)V = 42.39

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