Does deriving the formula for volume of any 3d object give us the formula for its surface area? (1 Viewer)

[yellowhighlighterr]

See above

 

[idkkdi]

See above

consider a cube

 

[SMARTYPANTS_SINGH]

I know this is the case for a sphere, but I am not sure it applies to every 3-dimensional shape.

 

[ZakaryJayNicholls]

For shapes which can be represented as functions of a single variable, it is sometimes the case that the surface area formula is a scalar multiple of the derivative (for some scalar multiple constant).
EG1: Cube - VCube = x^3, VCube' = 3*(x^2), SACube = 2*(VCube') = 2*(3*(x^2)) = 6*(x^2)
EG2: Sphere - VSphere = (4/3)*pi*(x^3), VSphere' = 4*pi*(x^3), SASphere = 1*(VSphere') = 4*pi*(x^3)
There are a few other shapes for which this logic or similar logics holds, but once you get to shapes represented as functions of two (o more) variables it becomes more complicated.

 

[yellowhighlighterr]

For shapes which can be represented as functions of a single variable, it is sometimes the case that the surface area formula is a scalar multiple of the derivative (for some scalar multiple constant).
EG1: Cube - VCube = x^3, VCube' = 3*(x^2), SACube = 2*(VCube') = 2*(3*(x^2)) = 6*(x^2)
EG2: Sphere - VSphere = (4/3)*pi*(x^3), VSphere' = 4*pi*(x^3), SASphere = 1*(VSphere') = 4*pi*(x^3)
There are a few other shapes for which this logic or similar logics holds, but once you get to shapes represented as functions of two (o more) variables it becomes more complicated.

Thanks!