Water cylinder

Zuzana poured 785 ml of water into a measuring cylinder with a base radius of 5 cm. The water in the cylinder reached a height of 2 cm from the upper edge of the cylinder. How tall is the cylinder? (π = 3.14)

Correct answer:

h =  12 cm

Step-by-step explanation:

$$\begin{gathered} r=5\text{ cm } \\ V=785\text{ ml}\to \text{ l}=785\mathrm{/}1000\text{ l}=0.785\text{ l } \\ x=2\text{ cm } \\ {V}_1=V\to {\text{cm}}^3=V\cdot 1000{\text{cm}}^3=0.785\cdot 1000{\text{cm}}^3=785{\text{cm}}^3 \\ S=\pi \cdot r^2=3.1416\cdot 5^2\doteq 78.5398{\text{cm}}^2 \\ {h}_1=V_1\mathrm{/}S=785\mathrm{/}78.5398\doteq 9.9949\text{ cm } \\ h=h_1+x=9.9949+2=12\text{ cm} \end{gathered}$$

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