Question

The base of a prism is a regular hexagon. If every edge of the prism measures 1 meter, then the volume of the prism is:
A) $\dfrac{3 \sqrt{2}}{2}\;\text{m}^3$
B) $\dfrac{3 \sqrt{3}}{2}\;\text{m}^3$
C) $\dfrac{6 \sqrt{2}}{2}\;\text{m}^3$
D) $\dfrac{5 \sqrt{3}}{2}\;\text{m}^3$

Answer 1

Hint: We will first determine the values of the length of each edge of the regular hexagon and the height of the prism. We will then substitute the value of length of each edge of regular hexagon and the height of the prism in the formula, \[V = \dfrac{{3\sqrt 3 }}{2} \times {a^2} \times h\] to find the volume of the required figure.

Complete step by step solution:
Since, every edge of a prism is 1 meter, it means that the length of each side of the hexagon is 1 meter and the height of the prism is 1 meter.
A prism with base as a regular hexagon is a three-dimensional solid shape which has 8 faces, 18 edges, and 12 vertices.
Volume of any three- dimensional solid shape is the amount of space enclosed by that shape.
Volume of Hexagonal prism is \[V = \dfrac{{3\sqrt 3 }}{2} \times {a^2} \times h\] , where $a$ is the length of side of the regular hexagon and $h$ is the height of the prism.
In this question, the length of each side of the hexagon is 1 meter and the height of the prism is 1 meter.
On substituting the value of $a = 1$ and $h = 1$ in the formula $V = \dfrac{{3\sqrt 3 }}{2} \times {a^2} \times h$ , we get,
$V = \dfrac{{3\sqrt 3 }}{2} \times {\left( 1 \right)^2} \times 1$
On solving the equation we get,
$V = \dfrac{{3\sqrt 3 }}{2}$
Hence, the volume of the required prism is $\dfrac{{3\sqrt 3 }}{2}{m^3}$.

Hence, option B is the correct answer.

Note: It is important to remember the formula of a regular prism to solve these types of questions. Also, height is not directly written in the question. Since every edge is of the same length, the height of the prism will be equal to the length of the edges.