Thinking outside of the box

My first approach

Yes, just place the center 3 inches above the paper. If that is a possibility?

Different rendering

To put it differently, if you like, you could draw a 5-inch-circle, use scissors to cut a radius, then form a cone by overlapping at the cutting line until the proportion of the height to the radius of the base is 3 to 4...

That will happen when the overlap covers $\frac{1}{4}$ of the surface of the cone...

Illustrations

To fully earn your votes, here is an illustration:

To see the situation from arbitrary angles, consult the following dynamic 3D-graph:

GeoGebra-illustration

In particular, see what it looks like from above - the $1:4$ proportion of the overlap becomes evident!