Assuming that the shape of the promastigote form of Leishmania can be approximated by a cylinder, then using (source: Wikipedia) length (x) of 15 (x1) to 30 (x2) micrometers (um), and radius (y) of 2.5 um, one obtains volumes V1 and V2 as follows:
V1 = pi * x1 * y**2 = 294.5 um**3
V2 = pi * x2 * y**2 = 589.0 um**3
Thus, the volume of a cylindrical promastigote would be approximately 300 to 600 um**3. The actual volume will be smaller by 30-50 % (just a guess) because the cell narrows and flattens toward both poles (see the second link).
Thanks a lot Martin for your effort and detailed response. However, I believe there are more variables than need to be considered. Such as the intracellular organelles (nucleus, mitochondria, kinetoplast etc). So basically I'm interested in know the volume of cytoplasm/cytosol of Leishmania.
I see. Then find out the counts and volumes of all those organelles (although I think both will vary) and subtract those numbers from the total cellular volume (which will also very and perhaps a lot --- see the attached link). There might also be a possibility to reconstruct the cell in 3D from scanning electron microscope images (maybe someone has already done that) and then one can play with various values of the variables to obtain the range and most probable value of the cytosolic volume at different environmental conditions and different stages of Leishmania life cycle.