Question

A solid with volume 8 cubic units is dilated by a scale factor of k to obtain a solid with volume v cubic units. Find the value of k to an image with each given volume

Answer 1

Answer:

$k=\frac{\sqrt[3]{v}}{2}$

Step-by-step explanation:

we know that

If two figures are similar, the 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 dilated solid

y------> the volume of the original solid

so

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

we have

$z=k$

$x=v\ units^{3}$

$y=8\ units^{3}$

substitute

$k^{3}=\frac{v}{8}$

$k=\frac{\sqrt[3]{v}}{2}$