Frink System Solver

Equations (one per line):
area = pi radius^2 volume = 4/3 pi radius^3 diameter = 2 radius mass = volume density
Solve for: (leave blank for all)
Show output as: Default Raw Frink notation MathML
Evaluate result numerically


radius === 1/2 diameter

radius === 1/2 (6 pi^-1 volume)^(1/3)

radius === ( -0.25000000000000005 - 0.4330127018922193 i ) (6 pi^-1 volume)^(1/3)

radius === ( -0.2499999999999999 + 0.43301270189221935 i ) (6 pi^-1 volume)^(1/3)

radius === 1/2 (6 density^-1 mass pi^-1)^(1/3)

radius === ( -0.25000000000000005 - 0.4330127018922193 i ) (6 density^-1 mass pi^-1)^(1/3)

radius === ( -0.2499999999999999 + 0.43301270189221935 i ) (6 density^-1 mass pi^-1)^(1/3)

radius === 1/2 ((4 area pi^-1)^(3/2))^(1/3)

radius === ( -0.25000000000000005 - 0.4330127018922193 i ) ((4 area pi^-1)^(3/2))^(1/3)

radius === ( -0.2499999999999999 + 0.43301270189221935 i ) ((4 area pi^-1)^(3/2))^(1/3)

density === mass volume^-1

density === 6 diameter^-3 mass pi^-1

density === 6 mass (4 area pi^-1)^(-3/2) pi^-1

density === 3/4 mass pi^-1 radius^-3

mass === density volume

mass === 1/6 density diameter³ pi

mass === 1/6 density (4 area pi^-1)^(3/2) pi

mass === 4/3 density pi radius³

diameter === 2 radius

diameter === (6 pi^-1 volume)^(1/3)

diameter === ( -0.5000000000000001 - 0.8660254037844386 i ) (6 pi^-1 volume)^(1/3)

diameter === ( -0.4999999999999998 + 0.8660254037844387 i ) (6 pi^-1 volume)^(1/3)

diameter === (6 density^-1 mass pi^-1)^(1/3)

diameter === ( -0.5000000000000001 - 0.8660254037844386 i ) (6 density^-1 mass pi^-1)^(1/3)

diameter === ( -0.4999999999999998 + 0.8660254037844387 i ) (6 density^-1 mass pi^-1)^(1/3)

diameter === ((4 area pi^-1)^(3/2))^(1/3)

diameter === ( -0.5000000000000001 - 0.8660254037844386 i ) ((4 area pi^-1)^(3/2))^(1/3)

diameter === ( -0.4999999999999998 + 0.8660254037844387 i ) ((4 area pi^-1)^(3/2))^(1/3)

area === 1/4 pi (6 pi^-1 volume)^(2/3)

area === 3/2 diameter^-3 (diameter³)^(2/3) volume

area === 3/16 radius^-3 (8 radius³)^(2/3) volume

area === 1/4 (6 density^-1 mass pi^-1)^(2/3) pi

area === 1/4 (diameter³)^(2/3) pi

area === 1/4 pi (8 radius³)^(2/3)

volume === density^-1 mass

volume === 1/6 diameter³ pi

volume === 1/6 (4 area pi^-1)^(3/2) pi

volume === 4/3 pi radius³

pi === 6 diameter^-3 volume

solve[pi (6 pi^-1 volume)^(2/3) === 4 area, pi]

pi === 3/4 radius^-3 volume

pi === 6 density^-1 diameter^-3 mass

solve[(6 density^-1 mass pi^-1)^(2/3) pi === 4 area, pi]

Evaluated result:

Sym	Symbolic?	Value
area =	area
density =	density
diameter =	diameter
mass =	mass
pi =	pi
radius =	radius
volume =	volume

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radius = 1/2 (6 density^-1 mass pi^-1)^(1/3)
       = 
3.242931562233897 cm



radius = ( -0.25000000000000005 - 0.4330127018922193 i ) (6 density^-1 mass pi^-1)^(1/3)
       = 
( -1.6214657811169488243 - 2.8084611156289109243 i ) cm



radius = ( -0.2499999999999999 + 0.43301270189221935 i ) (6 density^-1 mass pi^-1)^(1/3)
       = 
( -1.6214657811169478514 + 2.8084611156289112486 i ) cm



radius = 1/2 ((4 area pi^-1)^(3/2))^(1/3)
       = 
3.2410224072142885 cm



radius = ( -0.25000000000000005 - 0.4330127018922193 i ) ((4 area pi^-1)^(3/2))^(1/3)
       = 
( -1.6205112036071445741 - 2.8068077388821673853 i ) cm



radius = ( -0.2499999999999999 + 0.43301270189221935 i ) ((4 area pi^-1)^(3/2))^(1/3)
       = 
( -1.6205112036071436018 + 2.8068077388821677094 i ) cm



density = 6 mass (4 area pi^-1)^(-3/2) pi^-1
        = 
7012.377537620049669 m^-3 kg



mass = 1/6 density (4 area pi^-1)^(3/2) pi
     = 
0.99823490142200051056 kg



diameter = (6 density^-1 mass pi^-1)^(1/3)
         = 
6.485863124467794 cm



diameter = ( -0.5000000000000001 - 0.8660254037844386 i ) (6 density^-1 mass pi^-1)^(1/3)
         = 
( -3.2429315622338976486 - 5.6169222312578218485 i ) cm



diameter = ( -0.4999999999999998 + 0.8660254037844387 i ) (6 density^-1 mass pi^-1)^(1/3)
         = 
( -3.2429315622338957028 + 5.6169222312578224971 i ) cm



diameter = ((4 area pi^-1)^(3/2))^(1/3)
         = 
6.482044814428577 cm



diameter = ( -0.5000000000000001 - 0.8660254037844386 i ) ((4 area pi^-1)^(3/2))^(1/3)
         = 
( -3.2410224072142891482 - 5.6136154777643347705 i ) cm



diameter = ( -0.4999999999999998 + 0.8660254037844387 i ) ((4 area pi^-1)^(3/2))^(1/3)
         = 
( -3.2410224072142872036 + 5.6136154777643354187 i ) cm



area = 1/4 (6 density^-1 mass pi^-1)^(2/3) pi
     = 
0.0033038889377317506824 m²



volume = density^-1 mass
       = 
1/7000 m³



volume = 1/6 (4 area pi^-1)^(3/2) pi
       = 
0.00014260498591742864436 m³