Cylinder in a Cube

The cube has an edge length of 5 cm. This cube surrounds a rotating cylinder. Find the surface area of the shell and the volume of the cylinder.

Final Answer:

S =  111.0721 cm²
V =  196.3495 cm³

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ h=a=5\text{cm} \\ u=\sqrt{2}\cdot a=\sqrt{2}\cdot 5=5\sqrt{2}\text{cm}\doteq 7.0711\text{cm} \\ r=u/2=7.0711/2\doteq 3.5355\text{cm} \\ S=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 3.5355\cdot 5=111.0721{\text{cm}}^2 \end{gathered}$$

$V=\pi \cdot r^2\cdot h=3.1416\cdot 3.5355^2\cdot 5=196.3495{\text{cm}}^3$

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