Portioning ice cream

How many scoops of ice cream can we make using a scoop in the shape of a spherical canopy with a radius of 2.5 cm and a height of 4 cm. We have a 2-liter ice cream tub available. When portioning, we will follow the exact measure.

Correct answer:

n =  34

Step-by-step explanation:

$$\begin{gathered} r=2.5\text{cm} \\ h=4\text{cm} \\ V=2\text{l}\to {\text{cm}}^3=2\cdot 1000{\text{cm}}^3=2000{\text{cm}}^3 \\ {V}_1=\frac{1}{3}\cdot \pi \cdot h^2\cdot (3\cdot r-h)=\frac{1}{3}\cdot 3.1416\cdot 4^2\cdot (3\cdot 2.5-4)\doteq 58.6431{\text{cm}}^3 \\ n=\lfloor V/V_1\rfloor =\lfloor 2000/58.6431\rfloor =34 \end{gathered}$$

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