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)
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((length/2)^2+h^2)+
    width*sqrt((width/2)^2+h^2)+length*width
fig 3  Pyramid fig 4  Pyramid
   Volume = lwh/3    Reference: volume and surface area + formulas
   Surface Area = l√((l/2)²+h²)+w√((w/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
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)
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
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)
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
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)
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)
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
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
 
Reference:
Command List
   √ = sqr
   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
 
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Maxima Software - Computer Algebra System
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Documentation & Tutorial
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