Monday, October 19, 2015

Estimated Volume of the Giant Soup Can

         First, I measured the height of the bike in the photo from the bottom of the wheel to the handlebars. It has a height of about 5.5cm. Then, I measured the diameter of the water tank in the picture. It has a diameter of about 10.5cm. Then, I measured the height of an actual bike that looks the same size. Then, I found that it has a height of about 104cm if I measure it from the bottom of the wheel to the handlebars. Also, I measured the actual Campbells Soup can (540mL) in the refrigerator. It has a height of about 10.5cm and diameter of about 5.5cm.

         Using a ratio, I found the estimated diameter of the water tank.
diameter of the water tank in the photo : height of the bike in the photo = estimated diameter of the water tank : height of the actual bike of a similar size
-> 10.5cm : 5.5cm = x : 104cm -> x = 198.545cm = estimated diameter of the water tank

         Since the tank was in exactly the same proportions as a soup can, I found the estimated height of the water tank using a ratio as follows.
estimated diameter of the water tank : estimated height of the water tank = diameter of the actual soup can : height of the actual soup can
-> 198.545cm : y = 8.5cm : 11.5cm -> y = 268.620cm = estimated height of the water tank

         Therefore, the estimated volume of the water tank = area of the base * height = (estimated radius of the water tank)^2* π*estimated height of the water tank = (198.545/2)^2* π*268.620 = 8316606.156 cm^3 = 8316606.156 mL = 8316.606 L = 8.317 m^3 = 2197 gal

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