Block-shaped 4554

How many hectoliters of water can fit in a block-shaped tank with dimensions 24 m, 15 m, and 2 m deep? How many hectoliters of water must be drained so that the depth in the tank is only 15 dm? If the tank is full, how much water must be drained so that the level is 15 cm below the rim?

Correct answer:

V₁ =  7200 hl
V₂ =  18 hl
V₃ =  5.4 hl

Step-by-step explanation:

$$\begin{gathered} a=24\text{m} \\ b=15\text{m} \\ c=2\text{m} \\ {V}_0=a\cdot b\cdot c=24\cdot 15\cdot 2=720{\text{m}}^3 \\ {V}_1=V_0\to \text{hl}=V_0\cdot 10\text{hl}=720\cdot 10\text{hl}=7200\text{hl}=7200\text{hl} \end{gathered}$$

$$\begin{gathered} c_2=c-15/10=2-15/10=\frac{1}{2}=0.5\text{m} \\ {V}_2=a\cdot b\cdot c_2/10=24\cdot 15\cdot 0.5/10=18\text{hl} \end{gathered}$$

$$\begin{gathered} c_3=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ {V}_3=a\cdot b\cdot c_3/10=24\cdot 15\cdot 0.15/10=5.4\text{hl} \end{gathered}$$

Try another example