The Giant Soup Can of Hornby Island

This is an interesting problem as it teaches students a technique that they may not have seen before, estimation.

I.  Each Campbell's soup can is 51cm in height (h) and 41cm in width (w).
II.  We are given that the water tank can is in exactly the same proportions as a soup can.
III.  Assume that both cans are cylinders (i.e. ignore any lips, dents, or bulges)
IV.  The volume of a cylinder is given by: V = (pi)(r^2)(h).
V.  We are given the height of the bike in the photo.

from I, h = (51/41)(w) = (51/41)(2r) = (102/41)(r), since the width/diameter of a cylinder is equal to twice the radius, r.

from V, let the height of the bike be b meters.  The question now is, how much of the radius of the water tank can does b represent?  Assumptions:
- the bike wheels in the eyes of the camera are circular (i.e. the bike is not leaning)
- the bike's right handlebar is leaning against the tank (i.e. the bike is close to the tank)  
- the base of the bike wheels are below the base of the tank (if the ground were transparent)
Then it appears that b slightly less than r, so we are justified in setting b = (0.9)(r) as our estimate => r = (10/9)(b)

from II, III, and IV, the volume of the water tank can,
V_w = (pi)(r^2)(h).
         = (pi)(r^2)[(102/41)(r)]
         = (102/41)(pi)(r^3)
         = (102/41)(pi)[(10/9)(b)]^3
         = (102/41)(pi)[(1000/729)(b^3)]
         = (34000/9963)(pi)(b^3)

if b = 1 meter (estimate), then V_w = 10.7211 cubic meters.