A puzzle assignment on Nov. 12th

We can see that both the volunteer fire department and the actual Campbell’s soup can are likely cylinders. Here, we need to assume that we know the volume formula to calculate the exact volume of Campbell’s soup, which is V=pi*r^2*h.

 

 

Since we cannot carry a real Campbell’s soup to Hornby Island to determine the ratio, we use a bicycle as a reference here. We need to use the ratios between the actual Campbell’s soup and the bicycle, as well as the bicycle and the fire department, to determine the relative ratio between the actual Campbell’s soup and the fire department. Based on that, we can calculate the volume of the actual soup can and then use the ratio to approximate the volume of water that the fire department can hold here. However, when we approximate whether the water is sufficient to put out an average house fire, we need to consider the actual size of the house. Based on the various house sizes, we can then determine whether the water supply is sufficient or not.

Here is the calculation:

• -          The can volume is approximately equal to height  = 0.15m, radius  = 0.05m
• -           Bicycle length ratio to the actual can is 2:0.05 = 40:1, height ratio is 7:1.
• -          A bicycle‘s length is approximately 2m and height is approximately 1m.
• -          A fire department can hold around 3 bicycles here, which is around 6m long.
• -          A fire department can hold around 3 bicycles, which is around 3m tall.
• -          The volume of the fire department is approximately = pi* (3/2 m)^2 *6m = 42.41m^3 = 42410L

Using ratios is a standard method for performing approximate calculations in everyday life. For example, we can use the trigonometric functions and the angle to measure the tree that we observed.

-D is the distance between the person and the tree

-a is the angle to the top of the tree

-b is the angle to the bottom of the tree (if we do it from the ground, then we do not need to bother with measuring b)

So then we use the tan button on the calculator to find:

A = Tan a * D

B = Tan b * D

(We can also just estimate/measure B directly - if we are standing on level ground with the tree, it is the height of eyes or wherever measured, the angle from)

Height = A + B