Question

The base edge of a regular hexagonal prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm.
a. 1563.45
b. 1058.45
c. 1896.37
d. 1122.37

Answer 1

Hint: In order to solve this question, we need to remember that the volume of any prism is calculated as the product of the area of base and the height of the prism. And we also know that the area of regular hexagon I calculated by ${\displaystyle \frac{3\sqrt{3}}{2}}{a}^2$ where ‘a’ is the length of the edge. By using these concepts, we can solve this question.

Complete step-by-step answer:
In this question, we have been asked to find the volume of a regular hexagonal prism whose base edge is 6 cm and its bases are 12 cm apart. So, we can represent the question as shown below.

Now, we know that the volume of any prism is given by the product of the area of base and the height of the prism. So, for a regular hexagonal prism, we get the volume as,
Volume of the hexagonal prism = Area of the hexagonal base $\times$ Height of the prism
 Now, we know that area of hexagon is given by the formula, ${\displaystyle \frac{3\sqrt{3}}{2}}{a}^2$ where ‘a’ is the length of the edge of the hexagon. So, we can write the volume of the prism as,
${\displaystyle \frac{3\sqrt{3}}{2}}{a}^2\times \text{height of the prism}$
Now, we have been given the length of the base edge as 6 cm and also that the bases are 12 cm apart, that is, the height of the prism is 12 cm. So, we get the volume of the prism as,
${\displaystyle \frac{3\sqrt{3}}{2}}{\left(6\right)}^2\times 12$
Now, we will simplify it further to get the volume of the prism. So, we can write,
$\begin{array}{rl}& {\displaystyle \frac{3\sqrt{3}}{2}}\times 36\times 12\\ & {\displaystyle \frac{1296\sqrt{3}}{2}}\\ & 648\sqrt{3}\end{array}$
Now, we know that $\sqrt{3}=1.732$. So, we can write the volume of the prism as,
$\begin{array}{rl}& 648\times 1.732\\ & 1122.37c{m}^3\end{array}$
Hence, we get the volume of the regular hexagonal prism as $1122.37c{m}^3$. Therefore, option (d) is the correct answer.

Note: While solving this question, we can find the area of the regular hexagon by multiplying 6 with the area of the triangle OAB, as shown in the figure below.

Also, there are chances that we might make a calculation mistake in this question. So, we have to be very careful while solving this question.