Introduction: Kalkules Calculator Examples for geometric solids including calculations for cone, conical frustum, cube, cylinder, pyramid, rectangular prism, sphere, surface area and volume. Includes geometric formulas and shape diagrams. This may be used to check homework answers or practice problems.

 box  box
fig. 1  Box Volume fig. 2  Box Surface Area
   Volume = L*W*H    Surface Area = 2(L*W+L*H+W*H)
     reference: Wolfram Math World    Cuboid      reference: Ask Dr. Math: Drexel University    Box
     illustration: Box or Cuboid    cuboid    Volume = L*W*H
Kalkules does not use implied multiplication. For multiplication you need to include the multiplication operator (*).
 prism  prism
fig. 3  Triangular Prism Volume fig. 4  Triangular Prism Surface Area
   Volume = 1/2 (B*H)L
   Variables: B=4; H=3; L=5; S=3.6
   Surface Area = B*H + 2(L*S)+L*B
     reference: Wolfram Math World    Prism      reference: Ask Dr. Math: Drexel University    Prism
     from easy calculation    Prism Calculator
    From Wikipedia, the free encyclopedia    Triangular prism
     illustration:Triangular Prism    prism     Manual:    You do not need to use the multiplication character (*) in all cases. Some examples:
- before and after parenthesis: 4*(5+2) = 4(5+2) or (5+2)*4 = (5+2)4
- when a number precedes a variable or a constant: 4*a = 4a or 4*$pi = 4$pi
 piped  piped
fig. 5  Parallelpiped Volume fig. 6  Parallelpiped Surface Area
   Volume = L*W*H
   Variables: L=5; W=6; H=4
   Surface Area = 2(L*W+L*H+W*H)
     reference: Wolfram Math World    Parallelepiped      reference: Ask Dr. Math: Drexel University    Parallelepiped
     illustration: Parallelpiped    figure
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (The term rhomboid is sometimes used).
    Three equivalent definitions of parallelepiped are:
    The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces) are all specific cases of parallelepiped.
 pyramid  pyramid
fig. 7  Rectangular Pyramid Volume fig. 8  Rectangular Pyramid Surface Area
   Volume = L*W*H/3
   Variables: L=5; W=6; H=4
   Surface Area = L*sqrt((L/2)^2+H^2)+W*sqrt((W/2)^2+H^2)+L*W
     reference: Wolfram Math World    Pyramid      reference: Ask Dr. Math: Drexel University    Pyramid
     illustration: Pyramid    pyramid    Definition:
   A pyramid is a solid with a polygon base and connected by triangular faces to its vertex. A pyramid is a regular pyramid if its base is a regular polygon and the triangular faces are all congruent isosceles triangles.
 TPyramid  TPyramid
fig. 9  Topless Pyramid Volume fig. 10  Topless Pyramid Surface Area
   Volume = (h/3)*((L*W)+(c*d)+sqrt(L*W)*(c*d))
   Variables: L=5; W=6; c=3; d=2.5; h=4
   Surface Area = (2*(L+c)*h/2)+(2*(W+d)*h/2)+(L*W)+(c*d)
     reference: Wolfram Math World    Topless Pyramid      reference: Ask Dr. Math: Drexel University  Pyramid
     illustration:Topless Pyramid    TPyramid    Variables:
   A= Width (W) [base], B= Length (L) [base]
   c= Width [top], d= Length [top]
    Topless = Truncated or Frustum
Rectangular Pyramid Calculator
Solid Geometry
click me
Click on the picture
Free Lessons: Algebra 1:
1) Multiplying Fractions with Cross Canceling
2) Review of Exponents in Algebra
3) Add / Subtract Integers - Order of Operations
4) Algebraic Expressions, Terms, and Coefficients

    5) The Distributive Property in Algebra
    6) Introduction to Equations in Algebra
    7) Solving Multi-Step Equations in Algebra
    8) Simplifying Expressions in Algebra
 TriPyramid  TriPyramid
fig. 11  Triangular Pyramid Volume fig. 12  Triangular Pyramid Surface Area
   Volume = 1/12*sqrt(2)*a^2
   Variables: a= 3.6 (a = side b)
   Surface Area = sqrt(3)*a^2
     reference: Wolfram Math World    Triangular Pyramid   (tetrahedron)      reference: Ask Dr. Math: Drexel University    tetrahedron
From Wikipedia, the free encyclopedia    Tetrahedron
From Geometric Calculators    Tetrahedron Calculator
     illustration: Triangular Pyramid    TriPyramid    Manual:
    In Kalkules variables need not be only a character, "SurfaceArea" is a good name as well. And still, you can define as many variables as you want.
 cylinder  cylinder
fig. 13  Cylinder Volume fig. 14  Cylinder Surface Area
   Volume = $pi*r^2*h
   Variables: r=6; h=4
   Surface Area = 2*$pi*r^+2*$pi*r*h
     reference: Wolfram Math World    Cylinder      reference: Ask Dr. Math: Drexel University    Cylinder
     illustration: Cylinder    cylinder    Manual:
    Quadratic equation: A tool for calculating the roots of a quadratic equation. Enter the input values (a, b, c) and press the Calculate button. The output fields (x1, x2) will contain roots of the entered equation. If the equation has no real roots (D<0), complex roots will be calculated.
 cone  cone
fig. 15  Cone Volume fig. 16  Cone Surface Area
   Volume = $pi*r^2*h/3
   Variables: r=6; h=4
   Surface Area = $pi*r^2+$pi*r*sqrt(r^2+h^2)
     reference: Wolfram Math World    Cone      reference: Ask Dr. Math: Drexel University    Cone
     From Wikipedia, the free encyclopedia    Cone
     From Geometry Calculators    Cone Calculator
     illustration: Cone    cone    Manual:
    You can use an unlimited number of brackets in the expression.
   Variable names are not case-sensitive ( "volume" is the same as "Volume" or "VOLUME").

     Note: ^(1/2) = sqrt
 TCone  TCone
fig. 17  Topless Cone Volume fig. 18  Topless Cone Surface Area
   Volume = $pi*(R1^2+R1*R2+R2^2)*H/3
   Variables: R1=6; R2=3; H=4
   Surface Area = $pi*(R1+R2)*sqrt((R1-R2)^2+h^2)+$pi*(R1^2+R2^2)
     reference: Wolfram Math World    Topless Cone      reference: Ask Dr. Math: Drexel University    Cone
     From Geometry Calculators    Cone Frustum Calculator
     illustration: TCone    TCone    Manual:
    The expression notation consists out of numerals( 0 to 9, possibly A to F ), single-character operators ( +, -, *, etc... ), multi-character operators ( div, mod, nad ), functions ( f.i. sin ), variables ( f.i. radius ) and constants (f.i. $pi ).
click me
Click on the picture
Free Lessons: Algebra 1:
9) Natural Number Exponents
10) What is a Function in Algebra?
11) Multiplying Polynomials in Algebra
12) Factoring the Greatest Common Factor

    13) Digit Word Problems
    14) Age Word Problems
    15) Mixture Word Problems
 sphere  sphere
fig. 19  Sphere Volume fig. 20  Sphere Surface Area
   Volume = (4/3)*$pi*r^3
   Variables: r=6
   Surface Area = 4*$pi*r^2
     reference: Wolfram Math World    Sphere      reference: Ask Dr. Math: Drexel University    Sphere
     illustration: Sphere    sphere    Manual:
    Expression browser is a handy tool for storing commonly used expressions and mathematical formulas. It can be accessed from the main menu: View/Expression browser... .
   Alternate Formulas:    V=($pi*d^3)/6     A=$pi*d^2    d=2*r
 SphereC  SphereC
fig. 21  Spherical Cap Volume fig. 22  Spherical Cap Surface Area
   Volume = (($pi*h^2)/3)*(3*R-h)
   Variables: R=6; h=3
   Surface Area = 2*$pi*R*h
     reference: Wolfram Math World    Spherical Cap      reference: Ask Dr. Math: Drexel University    Sphere
     From Wikipedia, the free encyclopedia    Spherical cap
     From Geometry Calculators    Spherical Cap Calculator
     illustration: Spherical Cap    SphereC    Manual:
    To use an expression, simply select it and click the [Use] button. You can also add your own expressions, categories and even whole libraries. Also you can modify the standard libraries. All these tasks can be performed by right mouse click on the expression tree.
 spheroid  spheroid
fig. 23  Spheroid Volume fig. 24  Spheroid Surface Area
   Volume = $/3*$pi*a^2*c
   Variables: a=2, b=1, c=1, p= 1.6075
   Surface Area = 4*$pi[(a^(p)*b^(p)+a^(p)*c^(p)+B^(p)*c^(p))/3]^(1/p)
     reference: Wolfram Math World    Spheroid      reference: Ask Dr. Math: Drexel University    Sphere
     From Wikipedia, the free encyclopedia    Spheroid
     From Mathalino, Solid Geometry Review    Spherical Segment
 SphereSeg  SphereSeg
fig. 25  Sphere 2 Base Segment Volume fig. 26  Sphere 2 Base Segment Surface Area
   Volume = ($pi/6)*h*(3*a^2+3*b^2+h^2)
   Variables: R=6; h=3; a=6; b=4
   Surface Area = 2*$pi*R*h
     reference: Wolfram Math World    Spherical Segment      reference: Ask Dr. Math: Drexel University    Sphere
     From Wikipedia, the free encyclopedia    Spherical Segment
     From Mathalino, Solid Geometry Review    Spherical Segment
     illustration: Sphere 2 Base Segment    SphereSeg    Manual:
    If you are not sure, if the expression will be evaluated in the right order, use brackets. To check the written expression for errors, it is advisable to use the Expression preview tool
click me
Click on the picture
Free Lessons: Algebra 2:
1) The Slope of a Line
2) Writing Equations of Lines
3) Simplifying Radical Expressions in Algebra
4) Multiplying Radical Expressions in Algebra

     5) Transformation of Functions
     6) Inverses of Functions
     7) Zeros of Polynomials
     8) Introduction to Sequences
 SphereC  SphereC
fig. 27  Spherical Cone Volume fig. 28  Spherical Cone Surface Area
   Volume = (2/3)*$pi*R^2*h
   Variables: s=4; h=3; R=6
   Surface Area = $pi*R*(2*h+s)
     reference: Wolfram Math World    Spherical Cone      reference: Ask Dr. Math: Drexel University    Sphere
     From GlobalSpec     Sphere Sector Calculator
     From Mathalino, Solid Geometry Review     Spherical Cone
     illustration: Spherical Cone    SphereC    Manual:
    Select View/Variables... from the main window, fill in the variable values. If the variable form does not contain all the variables, click on the Refresh button.
 SphereSec  SphereSec
fig. 29  Spherical Sector Volume fig. 30  Spherical Sector Surface Area
   Volume = (2/3)*$pi*r^2*h
   Variables: h=3; r=6
   Surface Area = 2*$pi*r*h
     reference: Wolfram Math World    Spherical Sector      reference: Ask Dr. Math: Drexel University    Sphere
From Mathalino, Solid Geometry Review    Spherical Sector
     illustration: Spherical Sector   SphereSec    Manual:
    To view the constant window, select View/Constants... from the main menu.
Select the constant you want to use, and click on the Use button (you can also double-click on he constant)
 SphereWeg  SphereWeg
fig. 31  Spherical Wedge Volume fig. 32  Spherical Lune Surface Area
   Volume = ($pi/270)*r^3*d
   Variables: d=30 (degrees); r=6
   Surface Area = ($pi/90)*r^2*d
     reference: Wolfram Math World    Spherical Wedge      reference: Ask Dr. Math: Drexel University    Sphere
From Mathalino, Solid Geometry Review    Spherical Wedge
     illustration: Spherical Wedge   SphereWeg    Manual:
    To convert angles from decimal degrees to degrees, minutes and seconds, use the function dms(). For opposite conversion use the deg() function..
 Torus  Torus
fig. 33  Torus Volume fig. 34  Torus Surface Area
   Volume = 2*$pi^2*R*s^2
   Variables: s=2; R=6
   Surface Area = 4*$pi^2*R*s
     reference: Wolfram Math World    Torus      reference: Area and Volume Calculator    Online calculator: Torus
From Wikipedia, the free encyclopedia    Torus
From Planet Calc    Torus
     illustration: Torus   Torus    Manual:
    The setting dialog is available from the main menu: Preferences/Show preferences....
Default state: Settings on this tab define program state (selected number set, numeral system, etc.) right after start.
   √ = sqrt
   x² (or exponent 2) = ^2
   π = $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
   Basic Concepts in Plane Geometry
   Information on plane and solid geometric figures
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.
   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.
picture from
FREE TUTORIALS © copyright 2000-2013 @ Cadet Career Counseling all rights reserved
"Cadet Career Counseling" helping cadets make exceptional students.
Contact Webmaster at:(navyfalcon) e-mail