Cylinder volume diagonal

The axial section of the cylinder is a rectangle with a diagonal of u = 20 cm. The height of the cylinder is twice the diameter of the base. Calculate the cylinder volume in liters.

Final Answer:

V =  1.124 l

Step-by-step explanation:

$$\begin{gathered} u=20\text{cm}\to \text{dm}=20:10\text{dm}=2\text{dm} \\ h=2D=4r \\ {u}^2=h^2+(2r{)}^2 \\ {u}^2=(4r{)}^2+(2r{)}^2 \\ {u}^2=16r^2+4r^2 \\ {u}^2=20r^2 \\ r=u/\sqrt{20}=2/\sqrt{20}\doteq 0.4472\text{dm} \\ h=4\cdot r=4\cdot 0.4472\doteq 1.7889\text{dm} \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 0.4472^2\cdot 1.7889\doteq 1.124\text{l} \\ \text{ Verifying Solution: } \\ {u}_2=\sqrt{h^2+(2\cdot r{)}^2}=\sqrt{1.7889^2+(2\cdot 0.4472{)}^2}=2\text{dm} \\ D=2\cdot r=2\cdot 0.4472\doteq 0.8944\text{dm} \\ {h}_2=2\cdot D=2\cdot 0.8944\doteq 1.7889\text{dm} \end{gathered}$$

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