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

  SpeedCrunch colors the expression according to the syntax. You can easily distinguish numbers from variables. You can also see the matched parentheses.

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)

  SpeedCrunch has unlimited variable storage and more than 50 built-in math functions.

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 SpeedCrunch 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.
  There is a special variable, ans, which always holds the last calculation result.

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:
  Speed Crunch  does not use implied multiplication. For multiplication you need to include the multiplication operator.

    r = radius of cylinder
    h = height of cylinder

  In SpeedCrunch you do not need to memorize function names, use Ctrl+F to pop up a dialog where you can choose the function that you need.

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)

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 SpeedCrunch 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.

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

  In SpeedCrunch you can paste the expression from the clipboard, that you copied from somewhere else. And, you can quickly copy the last calculation result to the clipboard using Ctrl+R.

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.

  θ = angle in degrees

   Ref: Sphere formulas
   Ref: Spherical wedge formulas
   Ref: Spherical wedge formulas

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)

  SpeedCrunch Math book is a small library that contains the formula for 2D/3D objects and quadratic equations.

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.

  SpeedCrunch allows you to save your session so that you can resume from where you stopped the last time. Your history and variables will be intact the next time you load up the session.

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

   √ = Crtl + 1
   x² (or exponent 2) = F3 + 2
   π = Ctrl + P
Mathematical References and Formulas:
1300 Math Formulas
   Textbook on Math Formulas - Number Sets, Algebra, Geometry, Trigonometry, Matrices and Determinates, Vectors, Analytic Geometry, Differential Calculus, Integral Calculus, Differential Equations, Series, Probability
Geometric Shapes in Solid Geometry
   Shape diagrams and formulas for geometric solids including capsule, cone, conical frustum, cube, cylinder, hemisphere, pyramid, rectangular prism, sphere.
Handbook of Mathematics
   Calculator Operations, Calculator Usage, Special Keys, Algebra, Geometry, Trigonometry, Higher Concepts of Mathematics
SAT Test - Math
SparkNotes SAT Polygons
   Good news: Most polygons on the SAT have just four sides. You won’t have to tangle with any dodecahedrons on the SAT you take. There are five different types of quadrilaterals that pop up on the test. These five quadrilaterals are trapezoids, parallelograms, rectangles, rhombuses, and squares.
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
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.
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