Box  Box

Box (Rectangular Prism or Rectangular Solid)
From Calculator Soup   Box Calculator

Cuboid or Rectangular Prism
   A right rectangular prism is also called a cuboid, or a rectangular box. A right square prism is a square box. An equilateral square prism is a cube.

User Manual
   Ctrl+ENTER inserts end of line character.
   Button Del corresponds to Backspace key. Button C clears the edit boxes.
   After pressing ENTER or EXE, you can use cursor keys left / right to set cursor at the end or beginning of the input edit box.
   Command print is used to display numbers or text strings. The string is surrounded by quotation marks. Quotes inside the string must be doubled.
    There can be many expressions after the print keyword. They are separated by commas. Each print command usually produces one output line. But you can add a comma at the end of the command to disable the carriage return.

fig. 1  Box Volume fig. 2  Box Surface Area
   Volume = LWH    Surface Area = 2(LW+LH+WH)
     reference: Wolfram Math World    Cuboid      reference: Ask Dr. Math: Drexel University    Box
 pyramid pyramid

Rectangular Pyramid
From analyzemath   Pyramid Calculator

User Manual
 Variables: A name of a variable consists of letters, underscores, digits or characters that have ASCII code greater than 127. The first character must not be a digit. All names are case insensitive. The name of the variable can be as long as you want. You can create any number of variables if you have enough memory.
Precise Calculator does not use implied multiplication. For multiplication you must use the multiply operator (*). For Square Root (√) use "sqrt" or "^(1/2)" or "^(.5)

Pyramid faces
   The lower face ABCD is called the base and the perpendicular distance from the vertex, V, to the base at O is called the height of the pyramid. The distance from the vertex, V, to the base at M is called the slant height of the pyramid. The lateral surface of the pyramid is the sum of the area of its faces. The total surface area of a pyramid is the sum of the areas of its faces including its base.

   Apothem: The distance from the center of a regular polygon to the midpoint of one of its sides.
fig. 3  Rectangular Pyramid fig. 4  Rectangular Pyramid
   Volume = LWH/3
   Surface Area = L√((W/2)²+H²)+W√((L/2)²+H²)+LW
   reference: Wolfram Math World    Pyramid
   reference: Ask Dr. Math: Drexel University    Pyramid
 truncated pyramid    Topless Pyramid
   aqua-calc   Topless Pyramid Calculator  topless pyramid

   From Calculator Manual:
     /* this will be printed on 2 lines */
     print "add", 2+3; print "mult", 2*3
     /* this will be printed on 1 line */
     print "add", 2+3,; print " mult", 2*3
     /* insert blank line */
     print "add", 2+3; print; print "mult", 2*3

     hypot hypotenuse, hypot(a,b)=sqrt(a^2+b^2)

     Surface Area (ac) =1/2*(a+c)* slant(a) = 1/2*(a+c)* √(1/4*(b-d)²+h²)
     Surface Area (bd) 1/2*(b+d)* slant(b) =1/2*(b+d)* √(1/4*(a-c)²+h²)
     Surface Area (SA), Lateral = 2*SA(ac)+ 2*SA(bd)
   Surface Area (SA), Total = a*b+c*d+ (a+c)* slant(a)+ (b+d)* slant(b) = a*b+c*d+ (a+c)* √1/4*(b-d)²+h² +(b+d)* √1/4*(a-c)²+h²
fig. 5  Topless Pyramid Formula fig. 6  Topless Pyramid Reference
   Volume = (h/3)*((a*b)+(c*d)+sqrt(a*b)+(c*d))
   Surface Area = a*b+c*d+(a+c)*hypot(h,(b-d)/2+(b+d)*hypot(h,(a-c)/2
     reference: Wolfram Math World    Topless Pyramid
     reference: Ask Dr. Math: Drexel University    Topless Pyramid
 cylinder      Cylinder
   From Calculator City   Cylinder Calculator

   From User Manual: cylinder
     !=, <>    not equal
     >          greater than
     <           less than
     >=        greater than or equal to
     <=        less than or equal to

     gotor n    relative jump, gotor -1 jumps to the previous command, gotor1 jump to next command
     /* relative goto */
     a=1;b=7; if(a>b, 0, gotor4); print "a>b"; c=a; gotor3;
     print "a<=b"; c=b; print "c=", c

     goto n    jump to a label or to the n-th semicolon, goto0 jumps to the beginning
     /* goto label */
     a=6;b=5; if(a>b,0,goto label1); print "a>b"; c=a; goto end;
     label1: print "a<=b"; c=b; end: print "c=", c
fig. 7  Cylinder Formula
     Volume = pi*R^2*H   [piR²H]
     Surface Area = 2*pi*R*(R+H)   [2πR(R+h)]
fig. 8  Cylinder Reference
      Wolfram Math World    Cylinder
      Ask Dr. Math: Drexel University    Cylinder
 cone      Cone
   From Calculator City   Cone Calculator
  A cone is a geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex.

   From User Manual: cone
  There are two edit boxes. The upper one is used to enter mathematical expressions which are evaluated and the result is written to the lower edit box.
  The first edit box after the label "Precision:" holds number of significant digits. The checkbox "a/b" enables or disables fractions in the result
"inv" switches all buttons to their second function.
"hyp" changes sin,cos,tan buttons to sinh,cosh,tanh.
fig. 9  Cone
     Volume = pi*R^2*H/3   [piR²H/3]
     Surface Area = pi*R^2+pi*R*sqrt(R^2+H^2)   [πR²+πR√(R²+H²)]
fig. 10  Cone Reference
     reference: Wolfram Math World    Cone
     reference: Ask Dr. Math: Drexel University    Cone
 topless cone      Topless Cone
   From Calculator City   Cone Calculator
a truncated cone or pyramid; the part that is left when a cone or pyramid is cut by a plane parallel to the base and the top or apex part is removed.
   From User Manual: topless cone
     trunc   (integer part) trunc returns the integer part of a value; Example: x=trunc(4.67)=4
     frac   (fractional part) Frac returns the fractional part of an argument; Example: x=frac(4.67)=0.67
     round    round to the nearest integer
     ceil    round up (or take the ceiling, or round towards plus infinity)
     floor    round down (or take the floor, or round towards minus infinity)
     gcd    the greatest common divisor
     lcm    the least common multiple
     sort    sort items from lesser to greater
     sortd    sort items from greater to lesser

Volume & Surface area
V = pi * h * (R^2+r^2+R*r) / 3 = 263.89
SA = pi * (r * (r+l) + R * (R+l)) = 282.74
   R is radius of base circle
   r is radius of top circle
   h is height
   l is apothem or slant height
fig. 11  Topless Cone
     Volume =pi*(R1^2+R1*R2+R2^2)*H/3   [π(R1²+R1R2+R2²)H/3]
     Surface Area =pi*(R2*(R2+s)+R1*(R1+s))   [π(R2(R2+s)+R1(R1+s))]
fig. 12  Topless Cone Reference
     reference: Wolfram Math World    Topless Cone
     reference: Ask Dr. Math: Drexel University    Cone
 sphere      Sphere
   From Calculator City   Sphere Calculator

   From Calculator Manual: #########
   There can be a label before any command. The label is a word which is ended by a colon. It can contain characters that are allowed in variables, but a label name can also begin by a digit. Command goto jumps to a label. The parameter after goto can be a label or a commandís sequence number or an expression. Example: goto abc-2 jumps two commands before label abc. Command goto(abc-2) jumps to the command which number is abc-2 where abc is a variable and not a label. Command goto0 jumps to the beginning. Command gotor N jumps forward or backward according to a sign of N that can be any integer expression.

   You can write more expressions in the input edit box. They are separated by semicolons. A semicolon at the end causes the result of the last expression to be ignored and not shown.
fig. 13  Sphere
     Volume = 4/3*pi*R^3   [4/3πR³]
     Surface Area = 4*pi*R^2   [4πR²]
fig. 14  Sphere Reference
     reference: Wolfram Math World    Sphere
     reference: Ask Dr. Math: Drexel University    sphere
 spherical cap      Spherical Cap
   From Calculator City   Spherical Cap

   From Calculator Manual: SphericalCap
You can create submenus in the menu Macro. Rename a macro and use the backslash character to separate a submenu name and an item name.

   A comment starts with /* and ends with */. It is used especially in macros. It is ignored during computation. Comments cannot be nested.
fig. 15  Spherical Cap
     Volume = (pi/3)*H^2*(3*R-H)   [(π/3)h²(3R-h)]
     Surface Area =2*pi*R*H   [2πRH]
fig. 16  Spherical Cap Reference
      Wolfram Math World    Spherical Cap
     reference: Ask Dr. Math: Drexel University    sphere
 spherical segment      Spherical Segment
   From Calculator City   Spherical Segment
     Volume = (pi/6)*H*(3*a^2+3*b^2+H^2)    [(?/6)h(3a≤+3b≤+h≤)]
     Surface Area = 2*pi*R*H   [2?RH]

   From Calculator Manual: #########
Assignments to variables should be at the beginning of a formula. Example: volume of a cylinder r=1;v=2;v*pi*r^2. Then you use keyboard shortcuts Ctrl+1 and Ctrl+2 to change values of variables r, v.
Allowed characters are letters (case insensitive), digits, underscore and characters which have ASCII code greater than 127. Name must not start with a digit.
You can create any number of variables if you have enough memory. Postfix operators ++ and -- are used to add or subtract one to a variable.

     reference: Wolfram Math World    Spherical Segment
     reference: Ask Dr. Math: Drexel University    sphere
fig. 17  Spherical Segment fig. 18  Spherical Segment Reference
       Volume = (pi/6)*H*(3*a^2+3*b^2+H^2)   [(π/6)h(3a²+3b²+h²)]
     Surface Area = 2*pi*R*H   [2πRH]
V = 2/3 * pi * R^2 * h S = pi * R * (2h + r) R = the radius of the sphere r = the radius of the 'cone' part (the radius of the cone part where you put the icecream) h = the height of the spherical cap which extends above the end of the cone. (the height of the icecream part above your cone)
 Spherical Cone      Spherical Cone
   From Calculator City   Spherical Cone
A solid consisting of the cap and cone formed by the intersection of a plane with a sphere, the cone extending from the plane to the center of the sphere and the cap extending from the plane to the surface of the sphere. V=2/3piR^2h The surface area of a closed spherical sector is S=piR(2h+r),
   From Calculator Manual: Spherical Cone
for(x,a,b,f(x)) values from a to b are assigned to variable x and command f is executed, result is 0, f can modify variables, f can contain command if, return, ...

fig. 19  Spherical Conefig. 20  Spherical Cone Reference
     reference: Wolfram Math World    Spherical Cone
     reference: Ask Dr. Math: Drexel University    sphere
   Volume = (2/3)?R≤H    Surface Area = ?R(2h+r)
     reference: Wolfram Math World    Spherical Cone      reference:Ask Dr. Math: Drexel University    Sphere
 spherical sector      Spherical Sector
   From Global Spec   Spherical Sector

   In geometry, a spherical sector is a portion of a sphere defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap.

   From Users Manual: spherical sector
   Assignments to variables should be at the beginning of a formula. Example: volume of a cylinder r=1;v=2;v*pi*r^2. Then you use keyboard shortcuts Ctrl+1 and Ctrl+2 to change values of variables r, v.

   Real numbers, complex numbers, fractions, vectors and matrices can be stored to variables. Names of variables are not case sensitive.
fig. 21  Spherical Sector
     Volume = 2/3*pi*R^2*H   [(2/3)πR²H]
     Surface Area = 2*pi*R*H   [2πRH]
fig. 22  Spherical Sector Reference
     reference: Wolfram Math World    Spherical Cone
     reference: Ask Dr. Math: Drexel University    sphere
  v=4/3(pi r^3) A=4pi r^2
 spherical wedge      Spherical Wedge
   From Circle Sphere Math Calculator   Spherical Wedge
spherical wedge
In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's base). The angle between the radii lying within the bounding semidisks is the dihedral angle of the wedge (a).    From User Manual: 
   /* last expression is printed automatically */
      a=2; b=3; c=a*b
   /* last expression is not printed if there is a semicolon at the end */
      a=2; b=3; print c=a*b; d=a+b;
   /* print 2 blank lines */
fig. 23  Spherical Wedge
     Volume = (pi/270)*r^3*a   [(π/270)r³a]
     Surface Area = (pi/90)*r^2*a   [(π/90)r²a]
fig. 24  Spherical Wedge Reference
     reference: Wolfram Math World    Spherical Wedge
     reference: Ask Dr. Math: Drexel University    sphere
Macros (programs) of 3-D figures
Just copy the program - then paste it into Precise Calculator. You can change the values or lists. Then run the program.

 CYLINDER (do not copy title "CYLINDER")
H=4; R=6; print "Cylinder";
  print " volume= ",pi*R^2*H;
  print " surface area= ",2*pi*R*(R+H); print ""; print
" H= height of cylinder"; print " R= radius of cylinder"
Cylinder (solution: do not copy)
  volume= 452.3893421
  surface area= 376.9911184

    H= height of cylinder
    R= radius of cylinder
 SPHERICAL CAP (do not copy title "SPHERICAL CAP")
r=6; h=3; print "Spherical Cap"; print " volume=",(pi/3)
*h^2*(3*r-h); print " surface area=", 2*pi*r*h; print
"";print " r= radius of cap"; print " h= height of cap"
Spherical Cap (solution: do not copy)
  volume= 141.3716694
  surface area= 113.0973355

    r= radius of cap
    h= height of cap

 CONE (do not copy title "CONE")
R=6; H=4; print "Cone"; print " volume=", pi*R^2*H/3;
print " surface area=", pi*R^2+pi*R*sqrt(R^2+H^2);
print ""; print " R= radius"; print " H= height"
Cone (solution: do not copy)
  volume= 150.7964474
  surface area= 249.0234163

    R= radius
    H= height

 SPHERICAL CONE (do not copy title "SPHERICAL CONE")
r=4; h=3; R=6; print "Spherical Cone"; print "
volume=",2/3*pi*R^2*h; print " surface area=", pi*R*
(2*h+r); print ""; print " R= radius of sphere"; print "
r= radius of cone"; print " h= height of cap"
Spherical Cone (solution: do not copy)
  volume= 226.1946711
  surface area= 226.1946711

    R= radius of sphere
    r= radius of cone
    h= height of cap

 PYRAMID (do not copy title "PYRAMID")
L=5; W=6; H=4; print "Pyramid";
print " volume=",L*W*H;
print " surface area= ",L*sqrt((W/2)^2+H^2)+
W*sqrt((L/2)^2+H^2)+L*W;print""; print "
L= length of pyramid base"; print "
W= width of pyramid base";
print " H= height of pyramid"
 Pyramid (solution: do not copy)
  volume= 120
  surface area= 83.58495283

   L= length of pyramid base
   W= width of pyramid base
   H= height of pyramid
 TOPLESS CONE (do not copy title "TOPLESS CONE")
R1=6; R2=3; H=4; print "Topless Cone";
print " volume=",pi*(R1^2+R1*R2+R2^2)*H/3;
s=sqrt((R1-R2)^2+H^2);print " surface area=",pi*(R2*
(R2+s)+R1*(R1+s));print"";print" R1= large radius";
print " R2= small radius";print " H= height"

Topless Cone (solution: do not copy)
  volume= 263.8937829
  surface area= 282.7433388

    R1= large radius
    R2= small radius
    H= height

   ? = sqrt
   x≤ (or exponent 2) = ^2
   ? = pi
Mathematical References and Formulas:
   Kirt Blattenberger,Erie, PA, (814) 833-1967,
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.
Mathematical Formula Handbook PDF
   a compendium, of tables and formulas from various numerically and computationally orientated areas of mathematics
A First Book in Algebra by Wallace C. Boyden
   In preparing this book, the author had especially in mind classes in the upper grades of grammar schools
Algebra for Beginners
   Contents: Addition; Subtraction; The use of Double Signs and Brackets; Multiplication; Division; Simple Equations; The Lowest Common Multiple; Fractions; Quadratic Equations; Simultaneous Equations; Exponential Notation.
Algebra I
   an introduction to algebraic concepts for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.
Pyramid Volume and Surface Area
Total Surface Area of a Pyramid
   The total surface area of a pyramid is the sum of the areas of its faces including its base
Analyze Math Pyramid Problems
   Pyramid problems related to surface area and volume with detailed solutions.
Statistical References and Formulas:
   Electronic Statistics Textbook
statsoft textbook
  This Textbook offers training in the understanding and application of statistics. StatSoft has freely provided the Electronic Statistics Textbook as a public service.
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