Here is a modest curve shown with the three coordinate axes in three dimensions:

ID: 2894627 • Letter: H

Question

Here is the tube consisting all circles of radius 2 parallel to the xy-plane and centered on the curve. When you move each circle in its own plane so that it is centered on the z-axis, you get this:

Here they are side-by-side:

The cylinder has a base with radius 2, and the height of the cylinder is 3; so the volume of the cylinder measures out to
2^2 Pi 3 = 12 Pi cubic units.
Explain why the volume of the tube also measures out to 12 cubic units.

Here is a modest curve shown with the three coordinate axes in three dimensions:

Explanation / Answer

Since the cylinder made out of the tube having same height as that of tube and same radius as that of tube. The volume of tube = area of each circular strips multiplied by height and the formula will be valid for both cylinder as well as tube for calculations volume. Hence volume for cylinder and tube will be 2^2*pi*3.

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Here is a modest curve shown with the three coordinate axes in three dimensions:

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Explanation / Answer

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