Centimeters of water

A children's pool in the shape of a cylinder with a base diameter of d = 3 m contains V = 21 hl of water. How deep is it when the water reaches 10 cm below the edge?
State the result in centimeters and round to the nearest whole number.

Correct answer:

h =  40 cm

Step-by-step explanation:

$$\begin{gathered} d=3\text{m} \\ V=21\text{hl}\to {\text{m}}^3=21:10{\text{m}}^3=2.1{\text{m}}^3 \\ {c}_1=10\text{cm}\to \text{m}=10:100\text{m}=0.1\text{m} \\ r=d/2=3/2=\frac{3}{2}=1.5\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 1.5^2\doteq 7.0686{\text{m}}^2 \\ V=S_1\cdot c \\ c=V/S_1=2.1/7.0686\doteq 0.2971\text{m} \\ {c}_2=c+c_1=0.2971+0.1\doteq 0.3971\text{m} \\ h=c_2\to \text{cm}=c_2\cdot 100\text{cm}=0.3971\cdot 100\text{cm}=40\text{cm}=40\text{cm} \end{gathered}$$

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