Cuboid - box

The box has the shape of a cuboid with dimensions of 5 cm and 30 mm. Calculate the box's height if the cuboid's volume is 0.60 dm³. Calculate the surface area of ​​the box. (calculation of height from the volume, calculation of area from the formula, keep the same units)

Final Answer:

c =  40 cm
S =  670 cm²

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ b=30\text{mm}\to \text{cm}=30:10\text{cm}=3\text{cm} \\ {S}_1=a\cdot b=5\cdot 3=15{\text{cm}}^2 \\ V=0.60{\text{dm}}^3\to {\text{cm}}^3=0.60\cdot 1000{\text{cm}}^3=600{\text{cm}}^3 \\ V=S_{1}c \\ c=V/S_1=600/15=40\text{cm} \end{gathered}$$

$S=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (5\cdot 3+3\cdot 40+40\cdot 5)=670{\text{cm}}^2$

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