Bucket plastic material

The plastic bucket has the shape of a cylinder with a diameter of 25 cm and a height of 40 cm. How many square centimeters are needed to produce it? How many liters does it contain when filled 5 cm below the rim?

Final Answer:

S =  3632.4665 cm²
V =  17.1806 l

Step-by-step explanation:

$$\begin{gathered} d=25\text{cm} \\ h=40\text{cm} \\ r=d/2=25/2=\frac{25}{2}=12.5\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 12.5^2\doteq 490.8739{\text{cm}}^2 \\ {S}_2=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 12.5\cdot 40\doteq 3141.5927{\text{cm}}^2 \\ S=S_1+S_2=490.8739+3141.5927=3632.4665{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} V_1=S_1\cdot (h-5)=490.8739\cdot (40-5)\doteq 17180.5848{\text{cm}}^3 \\ V=V_1\to \text{l}=V_1:1000\text{l}=17180.5848:1000\text{l}=17.181\text{l}=17.1806\text{l} \end{gathered}$$

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