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=(1)/(3)b* 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

`\frac{\textup{BC}}{\textup{AC}}=\tan 60^\circ\\\\\Rightarrow (h)/(6)=\sqrt 3\\\\\Rightarrow h=6\sqrt 3.`

Therefore, the volume of the pyramid is

`V=(1)/(3)b* h=(1)/(3)* 54\sqrt 3* 6\sqrt 3=324.`

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