What is the dimension of the hypotenuse of the accompanying right triangle?
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<h3>Answer: 9V</h3>
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Reason:
The volume expression of a cone with radius r and height h is
Let's plug in the given height h = 12 and we'd get
This is the volume of the first cone. We're told the first cone has a volume of V, so we can say
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
The radius tripled which results in a volume that's 9 times bigger.