Answer:
If Franco wants to double the volume, he must multiply the radius and height of the original cone by [tex]\sqrt[3]{2}[/tex]
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 cone
y----> the volume of the original cone
so
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]x=2V\ units^{3}[/tex]
[tex]y=V\ units^{3}[/tex]
substitute and solve for the scale factor
[tex]z^{3}=\frac{2V}{V}=2[/tex]
[tex]z=\sqrt[3]{2}[/tex] ------> the scale factor
If Franco wants to double the volume, he must multiply the radius and height of the original cone by [tex]\sqrt[3]{2}[/tex]
