V=(1/3)pi*r^2*h, suppose r=h/2; which I don't understand why or how that is. And when I plug that in I get V=(1/3)pi*(h^3/4), but the book has (1/12)pi*h^3. I know its simple I'm just not seeing it.

Question

phi · Answer

you got
$$ V = \frac{1}{3} \pi \frac{h^3}{4} $$
you can multiply fractions:  top times top and bottom times bottom
you get
$$ V = \frac{1}{3} \pi \frac{h^3}{4} = \pi \frac{h^3}{12} $$
which you can write a few different ways:
$$ V = \frac{1}{12} \pi h^3 $$
or
$$ V = \frac{\pi h^3}{12}  = \frac{\pi }{12}h^3$$

phi · Answer

suppose r=h/2
which is the same as make the diameter (2 * r) equal to h
it means:  pick a height for the cone.  then make its diameter of the base the same length
(which you can do)
it looks roughly like this
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