Question

If the length, width, and height of a triangular prism are tripled, then the new volume is how many times the original volume?

• A. $13$
• B. $13$
• C. $27$
• D. $26$

Answer 1

The correct option is C $27$



Let $x,y,$ and $z$ be the dimensions of the original triangular prism as shown.
Volume of the original triangular prism $=V_1=$ Triangular base area $\times$ Height

$=(\frac{1}{2}\times y\times x)\times z$

$=\frac{yxz}{2}$

Volume of the triangular prism when its dimensions are tripled
$=V_2=\frac{\left(3y\right)\times \left(3x\right)\times \left(3z\right)}{2}=\frac{27yxz}{2}=27V_1$

Thus, the new volume is $27$ times the original prism.