TITLE: Sphere inside of a Sphere
QUESTION [5 upvotes]: I have a very interesting question.
I am given the fact that people like cookies the most when the ratio of cookie dough to chocolate is 1:1. The cookie is first placed on a sheet and has a diameter of one. The cookie is then covered in a layer of chocolate that's volume most match that of the cookie dough. It is a sphere inside of another sphere, with them having matching volumes. 
Please answer in fractional form
Thanks!

REPLY [4 votes]: Consider cookie as $3D$ object. So if corresponding $1D$ size of cookie + chocolate is $a > 1$ where $1D$ size of cookie is $1$, then $3D$ size of cookie with chocolate will be $a^3$.
Now, you have
$$ \frac{cookie + chocolate}{cookie} = \frac{a^3}{1} = 2 $$
Or
$$ a^3 = 2 $$
Therefore chocolate addition to diameter must be $\sqrt[3]{2} - 1$