Question

A regular triangular pyramid has an altitude of $9m$ and a volume of $187.06cu.m$. What is the base edge in meters?

• A. $12$
• B. $13$
• C. $14$
• D. $15$

Answer 1

The correct option is A $12$

Given : Altitude$\left(height\right(h\left)\right)=9m$, volume $=187.06cu.m$

We know that, Volume $=\frac{1}{3}Bh$, where $B=x^2\sin \theta$

$⟹187.06=\frac{1}{3}\left(\frac{1}{2}{x}^2\right(\sin \theta \left)\right)\left(9\right)$, where $x$ is base edge

$⟹187.06=\frac{1}{3}\left(\frac{1}{2}{x}^2\sin 60\right)9$

$⟹x^2=143.9988=144$

$\therefore x=12m$