Family 5

The Plavecký family built a pool which is 120 cm deep.

a/The bottom of the pool has a thickness of 10 cm, the side walls 20 cm. The pool has the shape of a cuboid with a base of 3 m x 5 m. How many cubic metres did they use for its construction?

b/Their son must clean its entire inner surface. In 10 min he cleans 0.5 m². How long will the entire cleaning take?

c/The depth of the water in the pool is 90 cm. How much water is in the pool?

Final Answer:

V =  5.868 m³
t =  300 min
V₃ =  13.5 m³

Step-by-step explanation:

$$\begin{gathered} a=3\text{m} \\ b=5\text{m} \\ c=120\text{cm}\to \text{m}=120:100\text{m}=1.2\text{m} \\ {h}_1=10\text{cm}\to \text{m}=10:100\text{m}=0.1\text{m} \\ {h}_2=20\text{cm}\to \text{m}=20:100\text{m}=0.2\text{m} \\ {a}_1=a+2\cdot h_2=3+2\cdot 0.2=\frac{17}{5}=3.4\text{m} \\ {b}_1=b+2\cdot h_2=5+2\cdot 0.2=\frac{27}{5}=5.4\text{m} \\ {c}_1=c+h_1=1.2+0.1=\frac{13}{10}=1.3\text{m} \\ {V}_1=a_1\cdot b_1\cdot c_1=3.4\cdot 5.4\cdot 1.3=\frac{5967}{250}=23.868{\text{m}}^3 \\ {V}_2=a\cdot b\cdot c=3\cdot 5\cdot 1.2=18{\text{m}}^3 \\ V=V_1-V_2=23.868-18=5.868{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} S=a\cdot b=3\cdot 5=15{\text{m}}^2 \\ Q=10/0.5=20{\text{min/m}}^2 \\ t=S\cdot Q=15\cdot 20=300\text{min} \end{gathered}$$

$$\begin{gathered} c_3=90\text{cm}\to \text{m}=90:100\text{m}=0.9\text{m} \\ {V}_3=a\cdot b\cdot c_3=3\cdot 5\cdot 0.9=13.5{\text{m}}^3 \end{gathered}$$

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