A survey is to be made with a chain or tape having its true length L and its incorrect length L'. Let the actual volume be V and measured volume be V'. Then, the correction for volume is given by:

Explanation:

If the chain that is employed for measuring length is not equal to the true length, then the length measured won't be correct. This measurement hence requires correction.

If, L = True length or designated length of the chain or tape

L' = Incorrect or Actual Length of the chain or tape used

The correction for length, area, and volume can be given by the following formulas.

Correction to Volume:

If V is the actual or the true volume and V' is the measured or the computed volume, then

True volume = Measured Volume x cube of [L'/L]

V = V' × (L'/L)3 ............(i)

Also,

L'/L = [(L +dL) / L] = 1 + (dL /L).........(ii)

dL = Error in the length of chain;

Let dL/L =e; Therefore Equations (ii) becomes

L'/L = 1+e therefore Equations (ii) becomes,

V = (1+e)(1+e)(1+e) × V;

By solving,

V = (1+3e)V'