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

Answer: (D)

$1122.37$

Given : Height $=6$ cm

Regular hexagon has all its sides of equal length.

So, length of sides is $6$ cm.

There will be total $6$ equilateral triangle, as there are six sides at the base of prism.

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

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

$=9\sqrt{3}$

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

$\therefore$ Base $=54\sqrt{3}$ sq.cm

Volume of prism $=$ base $\times$ height

$=54\sqrt{3}\times 12=1122.37$ cu. m

Hence, option D is correct.