Volume for a cone is 1/3 pi r^2h, where r is radius and h is height.
We have diameter = 1/2 radius. Thus, radius = 1.5in. We also have volume is 12 in.
Using formula for volume of a cone and plugging in what we know, we have
12 = 1/3pi(1.5)^2h, were solving for h.
To get, h= (123)/(pi*(1.5)^2), which is approximately 5.0931in, 5 inches