we can mesure the length of an curve using a wire?

Question

we can mesure the length of an curve using a wire
we can mesure the volume of an objet like a rock by putting it in water
but how can we mesure (not calculate) the surface of an object(not having a geometric form)?

Answer 1

You could paint the object, then see how much paint is used. Draw backs include inconsistant thickness of the paint.

Answer 2

We usually calculate this stuff because its not very convenient to deal with curves using cartesian measurements. But you can measure it using a very malleable grid and wrapping the object then counting the squares. You can make this by taking a cloth, and making a grid of small squares with a ruler. Then multiplying the pieces times the area of one square. Its really easy and if you make the squares small enough (depends on the curvature of the object) it will work well.

I am sure there are tons of ways but its all a matter of being creative.





But its generally faster to calculate it.

This is how you can calculate it:
if you took multivariable calculus you can use I believe its stokes theorem to use base surface to find the surface area.

Also, if you can find a curve which is consistantly rotated about the surface you can use some first year calculus to calculate the surface area by revolution.

Answer 3

One can measure the length of a curve by bending the wire along the curve, marking it at the endpoints, and then straightening out the wire and measuring between the endpoints.

Surfaces are harder,but depending on the surface, we can approximate it as something else. Is it like a cylinder, a prism, a cone> The surface of all those is understood. If nothing else, we can approximate the surface as a series of small triangles or rectangles, of which the surface are is well understood.