What if the RADIUS, not the HEIGHT, doubles??

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1

I have this problem summarized. Right circular cylinder, radius 5, height 4. Now imagine if the height gets doubled, the volume also doubles. But how to do this when the radius get doubled (because the radius is technically in parenthesis squared)???

Here is the formula for RCC: pi r^2 h = v

2

Think about it - what happens in the volume calculation when r is replaced with 2r? (hint: the volume is not multiplied by a factor of 2).

3

So is there actually a specific relationship? For example, I couldn’t find a relationship between pi 2^2 *3 (which equals 12pi) and pi 10^2 *3 (which equals 300pi).

4

@BeCambridge Yes - note that in your example, 10/2 = 5 and 300pi/12pi = 25 = 5^2.

Because the r is squared, the volume increases not by a factor of 2 (or whatever scale factor you put on the radius r) but instead by 2^2.

5

Thanks.