Calculate 4842

The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm.

Correct answer:

S =  62.8319 cm²

Step-by-step explanation:

$$\begin{gathered} u=5 \\ {S}_1=S/2 \\ {S}_1=\pi \cdot D\cdot h \\ {u}^2=h^2+D^2 \\ {S}_1=2\cdot S_2 \\ {S}_2=\pi \cdot (D/2{)}^2 \\ 2h=D \\ {u}^2=h^2+(2h{)}^2 \\ {5}^2=5h^2 \\ h=\sqrt{5^2/5}=\sqrt{5}\doteq 2.2361 \\ D=2\cdot h=2\cdot 2.2361=2\sqrt{5}\doteq 4.4721 \\ {S}_1=\pi \cdot D\cdot h=3.1416\cdot 4.4721\cdot 2.2361\doteq 31.4159 \\ {S}_2=\pi \cdot (D/2{)}^2=3.1416\cdot (4.4721/2{)}^2\doteq 15.708 \\ S=S_1+2\cdot S_2=31.4159+2\cdot 15.708=62.8319{\text{cm}}^2 \end{gathered}$$

Try another example