Answer: The correct option is
(C) [tex]2700\pi~\textup{units}^3.[/tex]
Step-by-step explanation: We are given to find the volume of the cone in the figure.
We know that the VOLUME of a cone with radius r units and height h units is given by
[tex]V=\dfrac{1}{3}\pi r^2h.[/tex]
From the figure, we note that
radius, r = 10 units and height, h = 81 units.
Therefore, the VOLUME of the cone will be
[tex]V\\\\\\=\dfrac{1}{3}\pi r^2h\\\\\\=\dfrac{1}{3}\pi\times 10^2\times 81\\\\\\=27\times 100\pi\\\\=2700\pi~\textup{units}^3.[/tex]
Thus, the volume of the cone is [tex]2700\pi~\textup{units}^3.[/tex]
Option (C) is CORRECT.
