Design & Drawing for Production Math

Area:

  • Rectangle:  A = bh

  • Parallelogram:  A = bh

  • Triangle:  A =  1/2 bh

  • Circle:  A = πr2

  • Cone:  A =  π x Diameter x Length ÷ 2

  • Sphere:  A = π x Diameter2

Volume:

  • Cylinder = πr2h

  • Rectangular Solid = whd

  • Pyramid = 1/3 x (Area of Base) x (Height)

  • Cone =  1/3 x (Area of Base) x (Height)

  • Sphere = 4πr3  / 3

  • 1 Cubic inch = 1.804 Fluid Ounces

  • Right Tri. Prism = 1/2 Base x Height

Surface Area:

  • Total Surface Area = Sum of all Exterior Surfaces

  • Prism = 2(wd + wh + dh)

  • Cylinder = 2πrh + 2πr2

  • Cone = πr2 + πrs

  • Sphere = 4πr2

Circumference:  C = πD

Mass = Volume x Density

Trigonometry:

  • Right Triangles

    • SOHCAHTOA

  • θ = angle

  • sin θ= opposite / hypotenuse

  • cos θ= adjacent / hypotenuse

  • tan θ= opposite / adjacent

Pythagorean Theorem:

Right Triangles

a2 + b2 = c2

Conversion:

  • Decimal Inches to Millimeters, multiply by 25.4

    2 in x 25.4 = 51mm
    .75 x 25.4 = 19mm

  • Millimeters to Decimal Inches, divide by 25.4

    75mm ÷ 25.4 = 2.95 in

    10mm  ÷ 25.4 = .39 in

Physics:

  • Density = mass/Volume; D = m/V

  • Total Distance =  average velocity/time; d=vt

  • Momentum = Mass * Velocity; p=mv

  • Work = Force * Distance; W=Fd

  • Power = Work / Time; P=W/t

  • Energy Transfer = Mass * Specific Heat * Change in temp.
    q=mc/\T

Units of Measurement:

Area:

  • Circle:  A = πr2

  • Ellipses: A = π(.5a)(.5b)  a = major axis,  b = minor axis

  • Triangle:  A =  .5(bh)

  • Rectangle:  A = LW or A = bh

  • Parallelogram:  A = bh

  • Multisided Polygons:  A = n s(.5f)
                                              2
              s = side length
         f = distance between flats or diameter of inscribed circle
         n = number of sides
     

  • Cone:  A =  π x Diameter x Length ÷ 2

  • Sphere:  A = π x Diameter2

  • Total Surface Area = Sum of the areas of all sides

Volume:

  • Cube:  V = S3  or V = wdh

  • Rectangular Prism:  V = wdh

  • Cylinder: V = πr2h

  • Pyramid: V = 1/3 x (Area of Base) x (Height)

  • Cone: V = π x radius2 x Height  / 3

  • Sphere: V = 4π x radius3  / 3

  • 1 Cubic inch = 1.804 Fluid Ounces

  • Right Tri. Prism: V = 1/2 Base x Height (Length)
     

  • Circumference:  C = πDiameter

Properties:

  • Mass (M) = Volume x Density

    • Metric = gram (g)

    • English = slug
       

  • Weight

    • Metric = Newton (N)

    • English = Pound (lb)
       

  • Weight = Mass x acceleration due to gravity

    • M = Mg

    • lbs = slugs x ft/sec2

    • Gravity (g) = 32.16 ft/sec2
       

  • Weight density (DW)

  • Weight = Volume x Weight Density

    • W = VDW
       

  • Surface Area (SA)

    • Cube:  SA = 6A

    • Rectangular Prism:  SA = 2(wd + wh + dh)

    • Cylinder:  SA = (2πr)h + 2(πr2)

Statistics:

  • Mean (Average) = Add up all the data, and then divide this total by the number of values in the data.

  • Mode = Number which occurs most often

  • Median = Put the numbers in order and find the middle number

  • Range = Subtract the lowest value from the highest value.