Question

The zone number of Universal Transverse Mercator (UTM) projection having a longitude of $67^\circ 20' 30''\text{E}$ is \underline{\hspace{1.2cm}} (In integer).

Hint:

UTM zones: $Z=\big\lfloor(\lambda+180)/6\big\rfloor+1$ with $\lambda$ in degrees (E positive, W negative). Each zone spans $6^\circ$ of longitude.

Answer 1

Step 1: UTM zone formula.
UTM zones are $6^\circ$ wide in longitude, numbered from $1$ at $180^\circ\text{W}$ eastwards.
For a longitude $\lambda$ (east positive), the zone number is \[ Z=\left\lfloor\frac{\lambda+180^\circ}{6^\circ}\right\rfloor+1. \] Step 2: Compute for $\lambda=67^\circ20'30''=67.3417^\circ$.
\[ \frac{\lambda+180^\circ}{6^\circ} =\frac{247.3417^\circ}{6^\circ}=41.2236\;⇒\; Z=\lfloor41.2236\rfloor+1=41+1=42. \] \[ \boxed{42} \]