Puzzle: The Giant Soup Can of Hornby Island

 My solution to the puzzle: 

Figure 1

1. The height of the bike is given. I will determine the length of the bike. That's because I can clearly see the ratio of the bike length to the tank length in the photo.

2. The size of the can is given. Measure the length a on the Soup can in centimeter. 

Find the ratio of length a to the height of the can. 

D

Which is the same ratio of the bike length to the tank length

3. Once we know the tank length, we could figure out the other dimensions of the tank by using proportions. We know that the dimensions of the soup can and the dimensions of the tank are in proportion.

Extension: 

Question: If every two people have to keep at least 2 arms length distance,  what is the maximum number of people allowed to be in an indoor basketball court? What is the max number of people allowed to be in a football stadium? Given the dimensions of the basketball court and Figure 2.

Figure 2

Solution:

We can see each person as a circle with a radius of 1 arm's length.  The first step, figure out the most efficient way to arrange these circles in a rectangle. 

Which way will you choose?

We know the room length and arm length. How many people are there in a row?

How many rows are there in an indoor basketball court? We can figure it out by finding the height of this equilateral triangle first.

Once we know the number of rows in an indoor basketball court, we can find the total number of people. 

Using the proportions and the figure, we can find the max number of people allowed in a football stadium.