Mug in Cube Box

A cylindrical mug is packed in a 1-liter cube paper box. The mug is in close contact with all the walls of the cube. What volume is my mug?

Final Answer:

V =  0.7854 l

Step-by-step explanation:

$$\begin{gathered} V_1=1{\text{dm}}^3 \\ {a}_1=\sqrt[3]{V_1}=\sqrt[3]{1}=1\text{dm} \\ r=a_1/2=1/2=\frac{1}{2}=0.5\text{dm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 0.5^2\doteq 0.7854{\text{dm}}^2 \\ V=S_1\cdot a_1=0.7854\cdot 1=0.7854\text{l} \end{gathered}$$

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