Question

A solid oblique pyramid has a regular hexagon base with an area of 54_/3 cm^2 and an edge length of 6cm. Angle BAC measures 60 degrees.
What is the volume of the pyramid?
A. 72_/3 cm^2
B. 108_/3 cm3
C. 324 cm^3
D. 486 cm^3

Answer 1

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

$V=\dfrac{1}{3}b\times h,$

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

$\dfrac{\textup{BC}}{\textup{AC}}=\tan 60^\circ\\\\\Rightarrow \dfrac{h}{6}=\sqrt 3\\\\\Rightarrow h=6\sqrt 3.$

Therefore, the volume of the pyramid is

$V=\dfrac{1}{3}b\times h=\dfrac{1}{3}\times 54\sqrt 3\times 6\sqrt 3=324.$

Thus, the required volume is $V=324~\textup{cm}^3.$ This makes (C) as the correct option.