Total surface area of a sphere cut into 16 identical pieces?

Question:

A solid sphere is cut into $$16$$ identical pieces with $$5$$ cuts.
Find the percentage increase in the new total surface area of all the pieces over that of the original sphere?

My try:

Initially I was confused about how to make such cuts on a sphere!
But then I was told that the cuts would be like an asterixis but with $$8$$ equally spaced spikes on the cross-section. The $$5^{th}$$ cut would be parallel to the table, thus dividing the sphere in $$16$$ identical pieces.
After this, for a piece, I was able to imagine and get the surface area of $$2$$ ($$1$$ curved and $$1$$ flat) out of the $$4$$ surfaces. I was unable to picturize mentally the rest of the $$2$$ (identical) faces.
The areas of those $$2$$ surfaces, $$1$$ curved and $$1$$ flat, would be $$\frac1{16}4\pi r^2$$ and $$\frac18\pi r^2$$ respectively.

I know the answer is $$250\%$$ but that wasn't really useful. I did trace back from there to find the area of the remaining $$2$$ surfaces but ended up using a lot of time though I should be using much less.
How to go about solving this question? Am I using the right approach?

• Imagine the cuts as circleso n the sphere Commented Jan 7, 2023 at 14:24

Every cut gives an additional surface equivalent with 2 times a full circle with radius $$r$$ (one circle at each side of the cut), imagine this when splitting a sphere exactly in half. So with 5 cuts you have in total 10 circle surfaces extra is $$10\pi r^2$$. The sphere was $$4\pi r^2$$, so the new surfaces are 250% of what you had.