Chapter E, Problem 12.12EX

To determine

To find: The correct option.

Answer to Problem 12.12EX

The option (A) is correct.

Explanation of Solution

Given information:

Given that the base of a right prism is a regular hexagon with side $4$ . And the height of the prism is $6$ .

Calculation:

Calculate the volume of the regular hexagon prism

  $V=\frac{3\sqrt{3}}{2}.a^2.h$

Substitute the values,

  $\begin{array}{c}V=\left(\frac{3\sqrt{3}}{2}\right)\left(4^2\right)\left(6\right)\\ V=\left(\frac{3\sqrt{3}}{2}\right)\left(16\right)\left(6\right)\\ V=3.48\sqrt{3}\\ V=144\sqrt{3}\end{array}$

Therefore, the correct option is (A).