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What if you have 3.14Pi?

Then you're so close to 10 that you can just use 10.

I actually did that on a physics exam once. Somehow I had a value with pi squared. I just replaced it with 10. I don't remember if I got that question right or wrong - I'm hard pressed to think of a situation where pi squared actually legitimately shows up.

Surface area of a Torus?

Not that I remember, or really relevant to undergrad physics - I'm pretty sure it was physics. Fusion and accretion disks are above my pay grade!

That's pretty much pi squared. Which, for weirdly good reason, is close to the value of G in meters per second squared.

only on this particular rock

Nope, on all rocks.

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