Answer: The answer is (C) 324 cubic cm.
Step-by-step explanation: As given in the question, given a solid oblique pyramid with a regular hexagonal base and area 54√3 cm². Also, the edge length of the base is 6cm and ∠BAC = 60°.
We are to find the volume of the pyramid.
The formula for finding the volume of a pyramid is given by
[tex]V=\dfrac{1}{3}b\times h,[/tex]
where, 'b' is the base area and 'h' is the perpendicular height of the pyramid.
Here, b = 54√3 cm², h = ?
Now, from the right-angled triangle ABC, we have
[tex]\dfrac{\textup{BC}}{\textup{AC}}=\tan 60^\circ\\\\\Rightarrow \dfrac{h}{6}=\sqrt 3\\\\\Rightarrow h=6\sqrt 3.[/tex]
Therefore, the volume of the pyramid is
[tex]V=\dfrac{1}{3}b\times h=\dfrac{1}{3}\times 54\sqrt 3\times 6\sqrt 3=324.[/tex]
Thus, the required volume is [tex]V=324~\textup{cm}^3.[/tex] This makes (C) as the correct option.
