Mammu and the Eiffel Tower
Last time we were in Paris Mammu and I, Mammu fell in love with the Eiffel Tower. She began to insist that we carry the Eiffel Tower back to India. I tried to explain to her that such a thing was impossible. But nothing would make her see reason. Finally I had to promise her that I would have an identical tower made in miniature, for her.
In order to have a smaller replica made I enquired the exact data of the Eiffel Tower Here are the details:
The Eiffel Tower is 300 metres high.
It is made of steel.
The weight of steel used is 8,000,000 kilograms.
I have decided to order the model to be made with only 1 kilogram of steel.
How high do you think my Eiffel Tower would be?
In order to have a smaller replica made I enquired the exact data of the Eiffel Tower Here are the details:
The Eiffel Tower is 300 metres high.
It is made of steel.
The weight of steel used is 8,000,000 kilograms.
I have decided to order the model to be made with only 1 kilogram of steel.
How high do you think my Eiffel Tower would be?
The model is 8000000 times lighter than the real Eiffel Tower. Both are made of the same metal, and so the volume of the model should be 8000000 times less than that of the real tower.
We know that the volumes of similar figures are to one another as the cubes of their altitudes.
Therefore, the model must be 200 times smaller than the original because 200 × 200 × 200 = 8,000000
The altitude of the real tower is 300 metres; and so the height of the model should be 300: 200 = 1½2 metres.
Then the model will be about the height of a man.
We know that the volumes of similar figures are to one another as the cubes of their altitudes.
Therefore, the model must be 200 times smaller than the original because 200 × 200 × 200 = 8,000000
The altitude of the real tower is 300 metres; and so the height of the model should be 300: 200 = 1½2 metres.
Then the model will be about the height of a man.
