GraphCalc - Box program commands

[Comment=   Box]
[PromptVal=length]
[PromptVal=width]
[PromptVal=height]
  volume=  length*width*height
  surface area= 2*(length*height+width*height+length*width)

Alternate Formulas:
fig 1  Box fig 2  Box
   Volume = LWH    Reference: Rectangular Prism calculation
   Surface Area = 2(LW+LH+WH)    volume    surface area
 
 GraphCalc - Pyramid program commands

[Comment=   Pyramid]
[PromptVal=length]
[PromptVal=width]
[PromptVal=height]
  volume= length*width*height/3
  surface area=  length*sqrt((width/2)^2+height^2)+
    width*sqrt((length/2)^2+height^2)+length*width

Alternate Formulas:
fig 3  Pyramid fig 4  Pyramid
   Volume = lwh/3    Reference: volume and surface area + formulas
   Surface Area = l√((w/2)²+h²)+w√((l/2)²+h²)+lw    Reference: Rectangular Pyramid online calculator
 
 GraphCalc - Topless Pyramid program commands

[Comment=   Topless Pyramid]
[PromptVal= a]   base length
[PromptVal= b]   base width
[PromptVal= c]   top length
[PromptVal= d]   top width
[PromptVal= h]   height
  volume= (h/3)*((a*b)+(c*d)+sqrt((a*b)*(c*d)))
  surface area=  (2*(a+c)*h/2)+(2*(b+d)*h/2)+a*b+c*d

Alternate Formulas:
fig 5  Topless Pyramid fig 6  Topless Pyramid
   Volume = (h/3)*((a*b)+(c*d)+√((a*b)*(c*d)))    Reference: Truncated Pyramid Volume
   Surface Area = (2(a+c)h/2)+(2(b+d)h/2)+ab+cd    Reference: Truncated Pyramid Surface Area
 
GraphCalc - Cylinder program commands

[Comment=   Cylinder]
[PromptVal=radius]
[PromptVal=height]
  volume= pi*radius^2*height 
  surface area= 2*pi*radius*(radius*height)

Alternate Formulas:
fig 7  Cylinder Volume fig 8  Cylinder Surface Area
   Volume = πR²h    Surface Area = 2πR(R+h)
 
GraphCalc - Cone program commands

[Comment=   Cone]
[PromptVal= radius]
[PromptVal= height]
  volume= (1/3)*pi*radius^2*height 
  surface area= pi*radius*sqrt(radius^2+height^2)+pi*radius^2

Alternate Formulas:
   surface area= pi*r(r + s)
   where r = radius, s = slant height
   s = sqrt(radius^2+height^2)
fig 9  Cone Volume fig 10  Cone Surface Area
   Volume = πR²h/3    Surface Area = πR√(R²+h²)+πR²
 
GraphCalc - Topless Cone program commands

[Comment=   Topless Cone]
[PromptVal=r1]
[PromptVal=r2]
[PromptVal=h]
  volume= pi*h/3*(r1^2+r2^2+r1*r2) 
  surface area= pi*(r1^2+r2^2+r1*r2)*sqrt(r1-r2)^2+h^2)

Alternate Formulas:  
fig 11  Topless Cone Volume fig 12  Topless Cone Surface Area
   Volume = πh/3(r1²+r2²+r1r2)    Surface Area = π(r1²+r2²+(r1r2)√(r1-r2)²+h²)
  GraphCalc - Sphere program commands

[Comment=   Sphere]
[PromptVal=radius]
  volume= 4/3pi*radius^3 
  surface area= 4*pi*radius^2

Alternate Formulas:
fig 13  Sphere Volume fig 14  Sphere Surface Area
   Volume = 4/3πR³    Surface Area = 4πR²
 
GraphCalc - Spherical Cap program commands

[Comment=   Spherical Cap]
[Comment= ]    blank line or space
[PromptVal=rs]    radius, sphere
[PromptVal=rc]    radius, cap
[PromptVal=h]    height, cap
  vol= ((pi*h^2)/3)(3rs-h)    using sphere radius (rs)
  vol= ((pi*h)/6)(3((rc)^2)+h^2)    using cap radius (rc)
  sa = 2*pi*rs*h    using sphere radius (rs)
Note: sa= surface area
Comment: volume using sphere radius and volume using cap radius should be the same (depends on accuracy of radius)

Alternate Formulas:
fig 15  Spherical Cap Volume & Surface Area fig 16  Spherical Cap
   Volume = (π*h²)/3)(3rs-h)    Reference: Spherical Cap Volume & Surface Area
   Surface Area = 2π*rs*h    Reference: Spherical Cap online calculator
 
GraphCalc - Spherical Cone program commands

[Comment=   Spherical Cone]
[Comment= ]    blank line or space
[PromptVal=rs]    radius, sphere
[PromptVal=rc]    radius, cone
[PromptVal=h]    height, cap
  vol= (2/3)pi*rs^2*h)    using sphere radius (rs)
  sa = pi*rs(2h+rc)     using sphere & cone radius (rs & rc)

Alternate Formulas:
fig 17  Spherical Cone Volume & Surface Area fig 18  Spherical Cone
   Volume = (2/3)*π*rs²h)    Reference: Spherical Cone Volume & Surface Area
   Surface Area = π*rs(2h+rc)    Reference: Spherical Cone
 
GraphCalc - Sphere 2 base Segment program commands

[Comment=   Sphere 2 base Segment]
[Comment= ]    blank line or space
[PromptVal=a]    radius, large
[PromptVal=b]    radius, small
[PromptVal=h]    height
  vol= (pi/6)h(3a^2+3b^2+h^2)
  sa = 2*pi*a*h

Alternate Formulas:
fig 19  Sphere 2 base Segment Volume & Surface Area fig 20  Sphere 2 base Segment
   Volume = (π/6)h(3a²+3b²+h²)    Reference: Sphere 2 base Segment Volume & Surface Area
   Surface Area = 2π*a*h    Reference: Sphere 2 base Segment
       Reference: Sphere 2 base Segment
 
GraphCalc - graph

[Comment=   graph sine, cosine, tangent]
[Comment= ]    blank line or space
[PromptVal y=]    sin (x)
[PromptVal y=]    cos (x)
[PromptVal y=]    tan (x)

Alternate Formulas:
fig 19  Graph sine (x)
Graph cosine (x)
fig 20  
       Reference: Trig graphs
       Reference: Graphs sin cos
       Reference: Sine function
 
Reference:
   Symbols to use for Graphing Purposes:
        Use a LOWER CASE x for the independent variable. GraphCalc will give you an error message if you try to use an upper case letter.
        Use the carat symbol ( ^ ) to indicate powers. For example, type x²  or  x³  as x^2 or as x^3.
        Use a forward slash ( / ) to indicate division. For example, type 2/3
        Use rational powers to indicate radicals. For example, type √(x)  as x^(1/2) or ³√(x) as x^(1/3).
        Enclose angles in trigonometric expressions in parenthesis [sin(x), cos(x), tan(x)].
        Use the Reciprocal Identities for secant(1/cos), cosecant(1/sin), and cotangent(1/tan).
        Graphing calculators and programs usually only use parenthesis. For example, in a mathematical text you will see {3+[x-5(x+1)]},
          but in a graphing calculator or program you must write (3+(x-5(x+1))).
Command List
   √ = sqrt or x^(1/2)
   x² (or exponent 2) = ^2
   π = pi
   PromptVal = prompt user to enter a value
   Commands will be enclosed in square brackets [ ]
   Comment lines will begin with [Comment=
 
Mathematical References and Formulas:
   rfcafe
   Kirt Blattenberger,Erie, PA, (814) 833-1967, rfcafe@earthlink.net
   Dr. math forum
   Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, 215-895-2000
   Handbook of Mathematics
   Calculator Operations, Calculator Usage, Special Keys, Algebra, Geometry, Trigonometry, Higher Concepts of Mathematics
 
Mathematical Software:
   Maxima Software - Computer Algebra System
   Maxima software is useful for manipulation of symbolic and numerical expressions, ordinary differential equations, polynomials, lists, systems of linear equations and sets.
   Documentation & Tutorial
   Designed for the new user Maxima by Example is a series of tutorial notes which include many examples of the power of Maxima.
 
Free Math eBooks:
   The Handbook of Essential Mathematics
   205 pages of mathematical formulas and other useful technical information that will serve both students and teachers. A pdf file.
   Handbook of mathematical, scientific, and engineering formulas
   covers the main fields of mathematics and focuses on the methods used for obtaining solutions. To accommodate different mathematical backgrounds,
   the preeminent authors outline the material in a simplified, schematic manner, avoiding special terminology wherever possible.
   Handbook of mathematics (1)
   Handbook of mathematics (2)
   The handbook includes a review of introductory mathematics and the concepts and functional use of Algebra, Geometry, Trigonometry and Calculus.
   Math Handbook of Formulas and Tables
   Students and research workers in mathematics, physics, engineering and other sciences will find this compilation of more than 2000 mathematical formulas and tables invaluable.
 
 
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