Okay this seems like a really simple question. Basically I'm adding together 8 spheres (like raindrops coalescing into one bigger drop) and I'm getting two different answers for the new radius.(adsbygoogle = window.adsbygoogle || []).push({});

Each individual drop is identical.

I start by expressing the new volume in terms of the individual drops' radii, and then the new radius. The individual drops' radii are R.

Volume = (4/3)∏(R)^3 * 8 = (4/3)pi(Rf)^3

I work it all out and find that the new radius is 2 times the radius of an individual drop. This is true according to a solution given.

But when I try this with surface area....

S.A. = 4∏(R)^2 * 8 = 4∏(Rf)^2

4∏ cancels,

then the new radius comes out as R*2*√(2)

What am I missing here? Is Surface area not additive, or am I making some calculation error?

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# Adding Spheres: How to find the new radius?

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