Introduction: AllerCalc has more than one hundred functions, including algebraic, transcendental, trigonometric, hyperbolic, engineering, statistical, and financial functions. It performs numerical integration, differentiation, and root-finding. It comes preloaded with a list of common physical constants found in science and engineering. You can store results in an unlimited number of variables.
 


 Box information and Reference

  A cube is a three-dimensional figure with six matching square sides. In a rectangular box, the length, width and height may be of different lengths.
 
    l = length of box
    w = width of box
    h = height of box

 You may assign values to variables which can then be used in subsequent calculations.
 The variables will be saved when the program exits and may be re-used in subsequent sessions.
The following commands may be used with variables:
  ShowVars: displays the variables' name and their values.
  ClearVars: deletes the variables and their values.

Ref. see AllerCalc Box

fig. 1  Box Volume
   Volume = l*w*h
   Surface Area = 2*(l*w+l*h+w*h)
fig. 2  Box Information and Reference
   Reference: Online Rectangular Solid Calculator
   Reference: Online Rectangular Prism Calculator

 


 Pyramid Information and Reference
   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.
    l = length of base
    w = width of base
    h = height of pyramid

  c and d = slant height of pyramid face (c= length face & d = width face)

  AllerCalc has unlimited variable storage and more than 100 built-in math functions.

Ref. see AllerCalc Pyramid

fig. 3  Pyramid Volume and Surface Area
   Volume = l*w*h/3
   Surface Area = l*c+w*d+l*w
   c=√((w/2)²+h²)    d=√((l/2)²+h²)
fig. 4  Pyramid Information and Reference
   Reference: Online Rectangular Pyramid Calculator
   Reference: Online Rectangular Pyramid Calculator
   Reference: Online Rectangular Pyramid Calculator

 


 Topless Pyramid Information and Reference

  A trunctated pyramid volume is one third the height times (A + sqrt(A*B) + B) where A and B are the area of the top and bottom faces.
  A= area (A*B) and B= area (C*D)

  In AllerCalc variables need not be only a character, "InterestRate" is a perfect name as well. And still, you can define as many variables as you want.
  
Ref. see AllerCalc Topless Pyramid

fig. 5  Topless Pyramid Volume and Surface Area
   Volume = (h/3)((a*b)+(c*d)+√((a*b)(c*d)))
   Surface Area = x+y+u    u=(a*b)+(c*d)
   x= 2*(a+c)*h/2    y= 2*(b+d)*h/2
fig. 6  Topless Pyramid Information & Reference
   Reference: Online Topless Pyramid calculator
   Reference: Online Geometric shapes Calculator
   Reference: Online Truncated Pyramid Calculator

 


 Cylinder Information and Reference
  A cylinder is a solid with two congruent circles joined by a curved surface.
  The expression: v = π*r²*h:
AllerCalc  does not use implied multiplication. For multiplication you need to include the multiplication operator.
When an expression begins with an operator (+, -, *, /, %, or !), the previous calculation result is used as the first operand for the operator. Example:
  2+2 =
4
+3 = (treated as ANS + 3, or 4 + 3)
7

    r = radius of cylinder
    h = height of cylinder

Ref. see AllerCalc Cylinder

fig. 7  Cylinder Volume & Surface Area
   Volume = π*r²*h
   Surface Area = 2*π*r(r+h)
  Note: 2πr*(r+h) = 2*πr² + 2*π*r*h
fig. 8  Cylinder Information & Reference
  Reference: cylinder volume
  Reference: cylinder formulas
  Reference:cylinder surface area


 

 Cone Information and Reference
   A circular cone has a circular base, which is connected by a curved surface to its vertex.
The vertex is the top or pointed area of the cone.

    r = radius of cone base
    h = height of cone
    l = slant height of cone (see diagram)
    l = √(r²+h²)

  Total Surface Area = Lateral Surface Area + Base Area
  Lateral Surface Area = π*r*√(r²+h²)
  Base Area = π*r²
  Total Surface Area = π*r²+π*r*√(r²+h²)

  Ref. see AllerCalc Cone

fig. 9  Cone Volume and Surface Area
   Volume = π*r²*h/3
   Surface Area = π*r²+π*R√(R²+h²)
fig. 10  Cone Information and Reference
   Reference: Cone formulas
   Reference: Cone Calculator
 


 Topless Cone Information and Reference

 L= Lateral Surface Area:
   L= pi*(R1+R2)*sqrt((R1-R2)^2+h^2)
 A= Total Surface Area
   A= pi*(R1+R2)*sqrt((R1-R2)^2+h^2)+pi*(R1^2+R2^2)
 V= Volume
   V= (pi*h/3)*(R1^2+R2^2+(R1*R2))

 
 Topless Cone = Cone Frustum
 Topless Cone = Truncated Cone

fig. 11  Topless Cone Volume
   Volume = πh/3(R1²+R2²+R1R2)
   Surface Area = π(R1+R2)√((R1-R2)²+h²)+π(R1²+R2²)
fig. 12  Topless Cone Information & Reference
   Reference: Truncated Cone
   Reference: Cone Frustum

 


 Sphere Information and Reference

A sphere is a solid with all its points equal distance from the center.


      r = radius of sphere

  In AllerCalc you just type the expression that you want to calculate and press Enter. You can see clearly what you typed along with the result in the scrollable display.

  Ref. see AllerCalc Sphere

fig. 13  Sphere Volume and Surface Area
   Volume = 4/3πr³
   Surface Area = 4πR²
fig. 14  Sphere Information and Reference
   Reference: Sphere Calculator
   Reference: Sphere Calculator

 


 Sphere 2 Base Segment Information and Reference

 
 a= large radius of segment
 b= small radius segment
 h= height of segment
 R= radius of sphere

Ref. see AllerCalc Sphere 2 Base Segment

fig. 15  Sphere 2 base segment Volume and Surface Area
   Volume = (π/3)h²(3R-h)
   Surface Area = 2πRh
fig. 16  Sphere 2 base segment Information and Reference
   Reference: Volume of a Spherical Segment
   Reference: Surface Area of a Spherical Segment

 


 Spherical Lune/Wedge Volume and Surface Area
Spherical Wedge the portion of a sphere included between two planes which intersect at the diameter.
portion of the surface of a sphere included between two great semicircles having a common diameter.
   A Spherical Lune is the surface area of a Spherical Wedge.

  a = angle in degrees

  
   Ref: Sphere formulas
   Ref: Spherical wedge formulas
   Ref: Spherical wedge formulas
Ref. see AllerCalc Spherical Lune/Wedge

fig 17  Spherical Lune/Wedge Volume and Surface Area
   Volume Spherical Wedge= (π/270)r³θ
   Surface Area Spherical Lune= (π/90)r²θ
fig 18  Spherical Lune/Wedge Information and Reference
   Reference: Volume of a Spherical Wedge  in degrees
   Reference: Surface Area of a Spherical Lune  in degrees

 


 Spherical Cap Information and Reference

  In geometry, a spherical cap is a portion of a sphere cut off by a plane.   The expression: A = 2*π*r*h:
     R = radius of sphere
     h = height of cap
     a = radius of the cap (or plane)

Ref. see AllerCalc Spherical Cap

fig. 19  Spherical Cap Volume and Surface Area
   Volume = πh²(3R-h)/3
   Surface Area = 2πRh
fig. 20  Spherical Cap Information and Reference
   Reference: Spherical Cap Calculator
   Reference: Spherical Cap


 

 Spherical Sector Information and Reference

  The part of a sphere between two right circular cones that have a common vertex at the center of the sphere, and a common axis.


Ref. see AllerCalc Spherical Sector

fig. 21  Spherical Sector Volume and Surface Area
   Volume = (2/3)πR²h
   Surface Area = 2πRh
fig. 22  Spherical Sector Information and Reference
   Reference: Spherical Sector
   Reference: Spherical Sector




AllerCalc Reference:

fig. 1/fig. 2  Box Volume and Surface Area
   'Box
     L=6, W=5, H=4
   v=L*W*H
     120
   a=2*(L+W+H)
     30
 

fig. 3/fig. 4  Pyramid Volume and Surface Area
   'Pyramid
     W=5, L=6, H=5
   c=sqrt((W/2)^2+H^2)
   d=sqrt((L/2)^2+H^2)
   v=L*W*H/3
     40
   a=L*c+W*d+L*W
     83.3019


fig. 5/fig. 6  Topless Pyramid Volume and Surface Area
   'Topless Pyramid
     a=6, b=5, h=4, c=3. d=2.5
   v=(h/3)*((a*b)+(c*d)+sqrt(a*b*c*d))
     70
   s=(2*(a+c)*h/2)+(2*(b+d)*h/2)+(a*b+c*d)
     103.5

fig. 7/fig. 8  Cylinder Volume and Surface Area
   'Cylinder
     r=6, h=5
   v=pi*r^2*h
     565.48667764
   a=2*pi*r*(r+h)
     414.69023027

fig. 9/fig. 10  Cone Volume and Surface Area
   'Cone
     r=6, h=5
   v=pi*r^2*h/3
     188.4955592
   a=pi*r^2+pi*r*sqrt(r^2+h^2)
     260.31707356
fig. 13/fig. 14  Sphere Volume and Surface Area
   'Sphere
     r=6
   v=4/3*pi*r^3
     904.77868423
   a=4*pi*r^2
     452.39834211

 
frus•tum
noun, plural frus•tums, frus•ta /Geometry.
1. the part of a conical solid left after cutting off a top portion with a plane parallel to the base.

trun•ca•ted (trngktd)
adj.
1. Having the apex (top portion) cut off and replaced by a plane, especially one parallel to the base. Used of a cone or pyramid.

ver•tex (vrtks)
n. pl. ver•ti•ces (-t-sz) also ver•tex•es
1. The highest point; the apex or summit: the vertex of a mountain.

 
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1300 Math Formulas
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Geometric Shapes in Solid Geometry
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Handbook of Mathematics
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SparkNotes SAT Circles
   A circle is the collection of points equidistant from a given point, called the center. A circle is named after its center point. The distance from the center to any point on the circle is called the radius, (r), the most important measurement in a circle.
SparkNotes SAT Triangles
   Triangles pop up all over the Math section. There are questions specifically about triangles, questions that ask about triangles inscribed in polygons and circles, and questions about triangles in coordinate geometry.
SparkNotes SAT Algebra
   
 
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