Glass cylinder height

A glass in the shape of a cylinder with a base diameter of 6 cm can hold 4 dl of water. Calculate the height of the glass and its surface.

Final Answer:

h =  14.1471 cm
S =  589.882 cm²

Step-by-step explanation:

$$\begin{gathered} D=6\text{cm} \\ V=4\text{dl}\to {\text{cm}}^3=4\cdot 100{\text{cm}}^3=400{\text{cm}}^3 \\ r=D/2=6/2=3\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3^2\doteq 28.2743{\text{cm}}^2 \\ V=S_1\cdot h \\ h=V/S_1=400/28.2743=14.1471\text{cm} \end{gathered}$$

$$\begin{gathered} S_2=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 3\cdot 14.1471=\frac{800}{3}\doteq 266.6667{\text{cm}}^2 \\ S=2\cdot (S_1+S_2)=2\cdot (28.2743+266.6667)=589.882{\text{cm}}^2 \end{gathered}$$

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