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The Volume of the cone will increase EIGHT times.

1st case,
consider the
diameter=2x cm⇒ radius=x cm 
height= h cm
Volume of the 1st Cone= \frac{1}{3}  \pi  r^{2} h
Putting the value we get,
Volume of 1st cone=  \frac{1}{3}  \pi x×h

2nd case, (since it gets double)
Consider the
Diameter= 4x⇒ radius= 2x cm
height= 2h cm
Putting the value we get,
Volume of 2nd cone=  \frac{1}{3}  \pi 4 x^{2} ×2h

Now divide the volume of 2nd Cone by 1st cone,
the answer remains is 8.
Hence, the volume increases by 8 times.
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