1 Answer

UnstableFractal · Answer 1 · 2023-08-24T17:00:52+0000

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Reason:

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

$(1)/(3)\pi*r^2*h$

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

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

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.

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