Answer: 9V
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Reason:
The volume expression of a cone with radius r and height h is
[tex]\frac{1}{3}\pi*r^2*h[/tex]
Let's plug in the given height h = 12 and we'd get
[tex]\frac{1}{3}\pi*r^2*h\\\\\frac{1}{3}\pi*r^2*12\\\\\left(\frac{1}{3}*12\right)\pi*r^2\\\\4\pi*r^2\\\\[/tex]
This is the volume of the first cone. We're told the first cone has a volume of V, so we can say [tex]V = 4\pi r^2[/tex]
We can't find the actual numeric volume because we don't know what value replaces r. So we leave it as is.
The second cone has the same height (h = 12) but the radius is now 3 times in size. Instead of r, we use 3r
Replace every copy of r with 3r. Then simplify
[tex]4\pi*r^2\\\\4\pi*(3r)^2\\\\4\pi*9r^2\\\\9(4\pi r^2)\\\\9V\\\\[/tex]
The radius tripled which results in a volume that's 9 times bigger.
