If we want

A children’s pool has the shape of a cylinder with a base diameter of 4 m and a depth of 50 cm (sketch, calculation, answer).

a) Calculate the volume of water in liters that can be in the pool if it is filled to the brim.
b) If we fill the pool only 75%, how many liters of water will be in the pool?
c) If we want to paint the walls of the pool twice, how large an area in m² does it need to be painted?

Correct answer:

V =  6283.1853 l
V₂ =  4712.389 l
S =  50.2655 m²

Step-by-step explanation:

$$\begin{gathered} d=4\text{m} \\ h=50\text{cm}\to \text{m}=50:100\text{m}=0.5\text{m} \\ r=d/2=4/2=2\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 2^2\doteq 12.5664{\text{m}}^2 \\ {V}_1=S_1\cdot h=12.5664\cdot 0.5\doteq 6.2832{\text{m}}^3 \\ V=V_1\to \text{l}=V_1\cdot 1000\text{l}=6.2832\cdot 1000\text{l}=6283.185\text{l}=6283.1853\text{l} \end{gathered}$$

$$\begin{gathered} r=75\%=\frac{75}{100}=\frac{3}{4}=0.75 \\ {V}_2=r\cdot V=0.75\cdot 6283.1853=4712.389\text{l} \end{gathered}$$

$$\begin{gathered} n=2 \\ {S}_2=\pi \cdot d\cdot h=3.1416\cdot 4\cdot 0.5\doteq 6.2832{\text{m}}^2 \\ S=n\cdot (S_1+2\cdot S_2)=2\cdot (12.5664+2\cdot 6.2832)=50.2655{\text{m}}^2 \end{gathered}$$

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