Question

the volume of a triangular prism is 42 cubic centimeters. what is the volume of a similar prism that is twice as large as large as the first prism

Answer 1

Answer:

The volume of the similar prism is $336\ cm^{3}$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> the volume of the larger prism

y----> the volume of the smaller prism

so

$z^{3}=\frac{x}{y}$

In this problem we have

$z=2$ -----> the scale factor

$y=42\ cm^{3}$

substitute and solve for x

$x=42(2^{3})=336\ cm^{3}$