Cylinder

In a 1-meter diameter cylinder is 1413 liters of water, which is 60% of the cylinder. Calculate the cylinder height in meters, do not write the units. The resulting value round and write as an integer.

Correct answer:

h =  3 m

Step-by-step explanation:

$$\begin{gathered} D=1\text{ m } \\ r=D\mathrm{/}2=1\mathrm{/}2={\displaystyle \frac{1}{2}}=0.5\text{ m } \\ V=1413\text{ l}\to {\text{m}}^3=1413\mathrm{/}1000{\text{m}}^3=1.413{\text{m}}^3 \\ V=\pi r^{2}h \\ {h}_1=V\mathrm{/}(\pi \cdot r^2)=1.413\mathrm{/}(3.1416\cdot 0.5^2)\doteq 1.7991\text{ m } \\ 0.60h=h_1 \\ h=h_1\mathrm{/}0.60=1.7991\mathrm{/}0.60=3\text{ m} \end{gathered}$$

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