Alice 2

Alice decided to plant geraniums in the spring. She bought one fifty-liter package of soil and also cuboid-shaped boxes with bottom dimensions of 1 m and 15 cm and a height of 17 cm. She wants to fill the boxes with soil only to a height of 2 cm from the top edge.

Calculate how many boxes in total Alice can fill with the purchased soil to the planned height.

Correct answer:

n =  2

Step-by-step explanation:

$$\begin{gathered} V=50\text{l}\to {\text{cm}}^3=50\cdot 1000{\text{cm}}^3=50000{\text{cm}}^3 \\ a=1\text{m}\to \text{cm}=1\cdot 100\text{cm}=100\text{cm} \\ b=15\text{cm} \\ c=17-2=15\text{cm} \\ {V}_1=a\cdot b\cdot c=100\cdot 15\cdot 15=22500{\text{cm}}^3 \\ {n}_1=V/V_1=50000/22500=\frac{20}{9}=2\frac{2}{9}\doteq 2.2222 \\ n=\lfloor n_1\rfloor =\lfloor 2.2222\rfloor =2 \end{gathered}$$

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