Boxes

Petra has planted flowers in two boxes in the shape of a cube. The first box has an internal dimension of 70 cm and the second 5 dm. She wants to make one box in the shape of a cuboid, into which she could transplant both flowers from these boxes. The new box is to have the same internal volume as both cube boxes together, two square side walls, and a height of 60 cm.

1. calculate in cm the length of the longest internal edge of the box that Petra wants to make
2. determine in litres the volume of soil that Petra will need to fill the new box up to the upper edge

Final Answer:

a =  88.3 cm
V₃ =  468 l

Step-by-step explanation:

$$\begin{gathered} x=70\text{cm} \\ y=5\text{dm}\to \text{cm}=5\cdot 10\text{cm}=50\text{cm} \\ c=60\text{cm} \\ {V}_1=x^3=70^3=343000{\text{cm}}^3 \\ {V}_2=y^3=50^3=125000{\text{cm}}^3 \\ V=V_1+V_2=343000+125000=468000{\text{cm}}^3 \\ V=a^2\cdot c \\ a=\sqrt{V/c}=\sqrt{468000/60}=10\sqrt{78}=88.3\text{cm} \end{gathered}$$

$V_3=V\to \text{l}=V:1000\text{l}=468000:1000\text{l}=468\text{l}=468\text{l}$

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