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!

  • 3
    $\begingroup$ Where is the sphere? Do you mean a circle? Also, what do you want the fractional form of? $\endgroup$ Dec 9, 2019 at 23:27
  • $\begingroup$ This sounds like a challenge for Claire Saffitz. $\endgroup$
    – TRiG
    Jan 6, 2020 at 17:41

2 Answers 2


If the inner sphere of dough has radius $r$ and when the outer shell of choclate has radius $R$ ... and we require the volume of dough & chocolate to be equal then \begin{eqnarray*} 2 \frac{4 \pi r^3}{3} = \frac{4 \pi R^3}{3}. \end{eqnarray*} So we require the ratio $R/r = \sqrt[3]{2}=1.2599 \cdots$. So a good approximation would be $ \frac{5}{4}$.

In other words if your ball of dough is $4$ units then when it is covered in chocolate make the radius increase to $5$ units.

Note that we rounded $1.2599$ down to $1.25$ so there will be slightly less chocolate ... so I would advise you to put an extra smidge of chocolate on in order to remedy this ... you can't put too much chocolate on your cookies!


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

$$ \frac{cookie + chocolate}{cookie} = \frac{a^3}{1} = 2 $$


$$ a^3 = 2 $$

Therefore chocolate addition to diameter must be $\sqrt[3]{2} - 1$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.