Question

A regular hexagonal pyramid whose base perimeter is $60cm$ has an altitude of $30cm$, the volume of the pyramid (in cu. cm)is:

• A. $2958$
• B. $2598$
• C. $2859$
• D. $2589$

Answer 1

The correct option is B $2598$

Given : Perimeter of regular hexagon $=60cm$ and height $=30cm$

We know that, regular hexagon has all its sides of equal length

$\therefore$ Perimeter $=6a=60cm$, where $a$ is side of hexagon

$⟹a=10cm$

There are exactly $6$ equilateral triangle

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

$=\frac{\sqrt{3}}{4}\times {10}^2=25\sqrt{3}$

$\therefore$ Area of $6$ equilateral triangles $=6\times 25\sqrt{3}=150\sqrt{3}$

$\therefore Areaofbase=150\sqrt{3}$

Volume $=\frac{1}{3}\times base\times height$

$=\frac{1}{3}\times 150\sqrt{3}\times 30$

$=1500\sqrt{3}=2598cu.m$

Hence, volume of pyramid is $2598cu.m$.