Pool model

The 1:500 scale pool model has internal dimensions of 15 cm, 10 cm, and 2.5 mm. Calculate how many hectoliters of water will be needed to fill a pool that will build according to this model.

Correct answer:

V =  46875 hl

Step-by-step explanation:

$$\begin{gathered} M=500 \\ a=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ b=10\text{cm}\to \text{m}=10:100\text{m}=0.1\text{m} \\ c=2.5\text{mm}\to \text{m}=2.5:1000\text{m}=0.0025\text{m} \\ A=M\cdot a=500\cdot 0.15=75\text{m} \\ B=M\cdot b=500\cdot 0.1=50\text{m} \\ C=M\cdot c=500\cdot 0.0025=\frac{5}{4}=1.25\text{m} \\ {V}_1=A\cdot B\cdot C=75\cdot 50\cdot 1.25=\frac{9375}{2}=4687.5{\text{m}}^3 \\ V=V_1\to \text{hl}=V_1\cdot 10\text{hl}=4687.5\cdot 10\text{hl}=46875\text{hl}=46875\text{hl} \end{gathered}$$

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