A cylindrical cup is used to fill a bowl

Hello Vjesus12.

Let's take a look at your question.

Volume of cylindrical cup: $$V_{cy}\ =\ \pi\cdot r^2\cdot h.$$ Volume of a hemisphere (bowl): $$V_{he}=\frac{2}{3}\cdot\pi\cdot R^3.$$ We have $$r=\frac{R}{2}\ \ \ \ and\ \ \ \ h=2\cdot r\ \leftrightarrow\ \ h=R.$$ Number of cups $$\frac{V_{he}}{V_{cy}}=\frac{\frac{2}{3}\pi\cdot R^3}{\pi\cdot r^2\cdot h}=\frac{\frac{2}{3}\pi\cdot R^3}{\pi\cdot\frac{R^2}{4}\cdot R}=\frac{\frac{2}{3}R^3}{\frac{R^3}{4}}=\frac{8}{3}\approx2.66667.$$ So, the maximum number of cups that can fill the bowl without overflowing is 2.

When the third cup is poured, the milk overflows.

So, the correct answer is A.

I hope this explanation may help you.

I'm available if you'd like a follow up.

Regards.