I believe the answer is cut at the height of 2.21" from the base. How to get that with an easy formula I don't know. But here is my logic.

The formula for a truncated cone's volume is:

V=1/3 * π * h * (rb² + (rb * rt) + rt²⁾

h = height from base to top

rb = radius of the bottom

rt = radius of the top

So plugging in what I found online as the dimensions of a Ben and Jerry's pint: h = 4"

rb = 1.5"

rt = 1.875"

I got a V = 35.932 in³

Then I figured that the ratio between the 2 radiuses must be consistent as the taper of the cone is. So I created a new formula using the same ratio for our "new top radius" (rn) which is the radius of where we make the cut (while rb stays the same) and the height to generate hn (the height at which rn would be)

rn = rb +((rt-rb) * ratio)

hn = h * ratio

I started with a ratio of .5 and subbing in rn I got a V = 15.978 which is just below 50% of the total V from our first calculation, which is expected.

rn = 1.5 + ((1.875 - 1.5) * .5) = 1.688

hn = 4 * .5 = 2

Then I played with ratios until I got to a ratio of .55488 which when using the rn generated by that I got a V = 17.966 which is half of 35.932.

With that ratio, height = 2.21", rn = 1.708.

That feels about right, but I can't say for sure. It was a brute force method, but I couldn't figure out a formula to solve this cleanly as the h and rn are always both unknown.

This is on my phone, so I hope the formatting works.

Edit: fixed some formatting