Question

Please help!! I’m not sure how to answer this question!!

Answer 1

Answer:  9V

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Reason:

The volume expression of a cone with radius r and height h is

$\frac{1}{3}\pi*r^2*h$

Let's plug in the given height h = 12 and we'd get

$\frac{1}{3}\pi*r^2*h\\\\\frac{1}{3}\pi*r^2*12\\\\\left(\frac{1}{3}*12\right)\pi*r^2\\\\4\pi*r^2$

This is the volume of the first cone. We're told the first cone has a volume of V, so we can say $V = 4\pi r^2$

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

$4\pi*r^2\\\\4\pi*(3r)^2\\\\4\pi*9r^2\\\\9(4\pi r^2)\\\\9V$

The radius tripled which results in a volume that's 9 times bigger.