Question

One hexagonal prism has dimensions that are triple the dimensions of a similar hexagonal prism. If the volume of the smaller prism is $4.75{\mathrm{cm}}^3$, what is the volume of the larger prism?

• A. $4.75{\mathrm{cm}}^3$
• B. $14.25{\mathrm{cm}}^3$
• C. $42.75{\mathrm{cm}}^3$
• D. $128.25{\mathrm{cm}}^3$

Answer 1

The correct option is D

$128.25{\mathrm{cm}}^3$

Explanation for the correct option:

Find the volume of a larger prism:

The volume of an hexagonal prism is $V=\frac{3\sqrt{3}{a}^{2}h}{2}$, where$a$ and $h$ are dimensions.

The volume depends on triple power of the dimensions. This means that the volume will be multiplied by $3^3,\mathrm{i}.\mathrm{e}.27$.

The volume of the smaller prism is $4.75{\mathrm{cm}}^3$. Therefore, the volume of the larger prism is,$27\times 4.75,i.e.128.25$.

Hence, the volume of the larger prism is $128.25{\mathrm{cm}}^3.$

Hence,option(D) is correct.