Question

The base of a right pyramid is an equilateral triangle of perimeter 8 cm and the height of the pyramid is $30\sqrt{3}$ cm. The volume of the pyramid is

• A. $160c{m}^3$
• B. $1600c{m}^3$
• C. $\frac{160}{3}c{m}^3$
• D. $\frac{5}{4}c{m}^3$

Answer 1

The correct option is A $160c{m}^3$

Volume of right pyramid $=$ $\frac{1}{3}\times areaofbase\times heightofpyramid$

Now, base is equilateral $△$, therefore,

area $=\frac{\sqrt{3}}{4}\times {\left(side\right)}^2$

Perimeter of triangle $=8cm$

$\therefore 3a=8\Rightarrow a=\frac{8}{3}cm$

$\therefore area=\frac{\sqrt{3}}{4}\times \frac{8}{3}\times \frac{8}{3}=\frac{16\sqrt{3}}{9}{cm}^2$

Now, Volume $=\frac{1}{3}\times \frac{16\sqrt{3}}{9}\times 30\sqrt{3}$

$=\frac{160\times 3}{9}=\frac{160}{3}{cm}^3$