Thinking outside of the box

geometry geometric-construction soft-question circles

Solution 1:

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:

enter image description here

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!

Related

Translations in two dimensions - Group theory
Integral $\int_0^1 \left(\arctan x \right)^2\,dx$
Pigeonhole Principle Question: Given any 5 points inside a square of side length 2, there is always a pair whose distance apart is at most $\sqrt2$
Examples of properties not preserved under homomorphism
Show that $A=0 \iff \operatorname{tr}(A)=0$ where $A= M_1+ \cdots +M_{\ell}$. [duplicate]
Why are 'differential operators on manifolds' differential operators?
Lie group, differential of multiplication map
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
Could trigonometry exist in one dimension?
Why does zero raised to the power of negative one equal infinity?
Finding n and k that satisfies ${n \choose k} = 517 $
How to prove that $A^2$ is a symmetric matrix?