If the dimensions of a cylinder are doubled, then its volume is quadrupled. The statement is false.
What is the volume of a right circular cylinder?
Suppose that the radius of the considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
The right circular cylinder is the cylinder in which the line joining center of the top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
If the dimensions of a cylinder are doubled, the radius will become 2r, and the height will become 2h.
Hence, the new volume is:
[tex]V = \pi r^2 h \: \rm unit^3\\\\V = \pi (2r)^2 (2h)\: \rm unit^3\\\\V = 8\pi r^2 h \: \rm unit^3[/tex]
So, compared to the old volume, the new volume is increased eight-fold.
Therefore, the statement is false.
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