Question

The bases of a right prism is a hexagon with one of each side equal to $6cm$. The bases are $12cm$ apart. What is the volume of the right prism (in ${cm}^3$)?

• A. $1211.6$
• B. $2211.7$
• C. $1212.5$
• D. $1122.4$

Answer 1

The correct option is D $1122.4$

Given : Height$\left(h\right)=12cm$, each side of hexagon Is $6cm$

There must be $6$ equilateral triangles in hexagonal prism.

Area of one equilateral triangle $=\frac{\sqrt{3}}{4}\times sid{e}^2$

$=\frac{\sqrt{3}}{4}\times 36=9\sqrt{3}$

$\therefore$ Area of $6$ equilateral triangles $=6\times 9\sqrt{3}=54\sqrt{3}$

We know that, volume of right prism $=base\times height$

$=54\sqrt{3}\times 12$

$=1122.4c{m}^3$

Hence, volume of right prism is $1122.4c{m}^3$.