Hectoliters 25821

The cistern of the public water supply has a cube-shaped interior. The edge of this cube is 5 m long.
a) How much water is in the reservoir when it is completely filled? (Express this volume in m³ and hectoliters. )
b) How high does the water reach in the reservoir when a certain amount of water has been drained from it, and 700 hl of water remains?

Correct answer:

V₁ =  125 m³
V₂ =  1250 hl
h =  2.8 m

Step-by-step explanation:

$$\begin{gathered} a=5\text{m} \\ {V}_1=a^3=5^3=125{\text{m}}^3 \end{gathered}$$

$V_2=V_1\to \text{hl}=V_1\cdot 10\text{hl}=125\cdot 10\text{hl}=1250\text{hl}=1250\text{hl}$

$$\begin{gathered} S=a^2=5^2=25{\text{m}}^2 \\ {V}_3=700\text{hl}\to {\text{m}}^3=700:10{\text{m}}^3=70{\text{m}}^3 \\ {V}_3=S\cdot h \\ h=V_3/S=70/25=2.8\text{m} \end{gathered}$$

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