PRECISE CALCULATOR Examples: Solid Geometric Figures calculation formulas with answers, diagrams and references for volume and surface area.
Figures include; Box, Pyramid, Topless Pyramid, Cylinder, Cone, Topless Cone, Sphere, Spherical Cap, Sphere 2 Base Segment, Spherical Cone, Spherical Sector.
Box (Rectangular Prism or Rectangular Solid) 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  
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 
Rectangular Pyramid User Manual 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 
Topless Pyramid aquacalc Topless Pyramid Calculator 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*(bd)²+h²) Surface Area (bd) 1/2*(b+d)* slant(b) =1/2*(b+d)* √(1/4*(ac)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*(bd)²+h² +(b+d)* √1/4*(ac)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,(bd)/2+(b+d)*hypot(h,(ac)/2 
reference: Wolfram Math World Topless Pyramid reference: Ask Dr. Math: Drexel University Topless Pyramid 
Cylinder From Calculator City Cylinder Calculator From User Manual: Conditions: !=, <> 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 nth 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 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: 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 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: 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 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 command’s sequence number or an expression. Example: goto abc2 jumps two commands before label abc. Command goto(abc2) jumps to the command which number is abc2 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 From Calculator City Spherical Cap From Calculator Manual: 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*RH) [(π/3)h²(3Rh)] 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 From Calculator City Spherical Segment Formula: Volume = (pi/6)*H*(3*a^2+3*b^2+H^2) [(?/6)h(3a²+3b²+h²)] 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 
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: 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 Cone  fig. 20 Spherical Cone Reference reference: Wolfram Math World Spherical Cone reference: Ask Dr. Math: Drexel University sphere 
Volume = (2/3)?R²H  Surface Area = ?R(2h+r) 
reference: Wolfram Math World Spherical Cone  reference:Ask Dr. Math: Drexel University Sphere 
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: 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 
Spherical Wedge From Circle Sphere Math Calculator 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: Print: /* 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 */ print;print;  
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 