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Question
Which one of the following has the infinite surface area but finite volume?
Which one of the following has the infinite surface area but finite volume?
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Solution
The correct option is A Gabriel’s horn
No such thing exists in the physical universe, but there is a mathematical construct called Gabriel’s horn, also known as the Torricelli's trumpet, which is infinitely long. Gabriel's horn is obtained by rotating a graph of the function, y = 1x from x = 1 to ∞ , about the x-axis.
The shape resembles a never-ending trumpet. We can calculate the surface area and volume of the figure using integral calculus. The result we get actually says that the figure has an infinite surface area but finite volume.
If such a thing were to really exist, you could fill it with paint but not paint it completely!
No such thing exists in the physical universe, but there is a mathematical construct called Gabriel’s horn, also known as the Torricelli's trumpet, which is infinitely long. Gabriel's horn is obtained by rotating a graph of the function, y = 1x from x = 1 to ∞ , about the x-axis.
The shape resembles a never-ending trumpet. We can calculate the surface area and volume of the figure using integral calculus. The result we get actually says that the figure has an infinite surface area but finite volume.
If such a thing were to really exist, you could fill it with paint but not paint it completely!
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