Answer:
[tex]k=\frac{\sqrt[3]{v}}{2}[/tex]
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
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=k[/tex]
[tex]x=v\ units^{3}[/tex]
[tex]y=8\ units^{3}[/tex]
substitute
[tex]k^{3}=\frac{v}{8}[/tex]
[tex]k=\frac{\sqrt[3]{v}}{2}[/tex]
The value of scale factor k, which is used to obtain a solid with volume v cubic units by 8 cubic unit is,
[tex]k={\dfrac{\sqrt[3]{v}}{2}\\[/tex]
Volume of solid is the amount of quantity, which is obtained by the solid or object in the 3 dimensional space.
The more the volume of a object is obtains the more space. Liter is the most common unit to measure the volume of a solid.
Given information-
The volume of the solid is 8 cubic units.
The scale factor of dilation is k.
The volume of new solid obtained is v.
Here the new volume of the solid is find out by the volume of 8 units and the scale factor k. Thus the scale factor k should be equal to the ratio of the volume of these two solid.
The volume of the solid is represents in cubic units. Thus,
[tex]k=\sqrt[3]{\dfrac{v}{8}}\\k={\dfrac{\sqrt[3]{v}}{2}\\[/tex]
Hence the scale value of scale factor k in terms of v is,
[tex]k={\dfrac{\sqrt[3]{v}}{2}\\[/tex]
Learn more about the volume of solid here;
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