Question

If the volume of a prism is $1920$ $\sqrt{3}c{m}^3$ and the side of the equilateral base is $16$ $cm$, then the height (in cm) of the prism is?

• A. $19$
• B. $20$
• C. $30$
• D. $40$

Answer 1

The correct option is C $30$

Volume of prism $=$ Area of equilateral triangle $\times$ height

Now, Area of triangle $=\frac{\sqrt{3}}{4}{a}^2$

= $\frac{\sqrt{3}}{4}{16}^2$ = $64\sqrt{3}$

$1920\sqrt{3}=64\sqrt{3}\times$ height

$\therefore$ height $=$ $\frac{1920}{64}$

$=30cm$