Aluminum cylinder

The aluminum cylinder weighs 1400 g and is 26 cm high. Its density is 2700 kg/m³. Calculate the base area of ​​the cylinder and express the result in cm².

Correct answer:

S =  451.4845 cm²

Step-by-step explanation:

$$\begin{gathered} m=1400\text{g} \\ h=26\text{cm} \\ \rho =2700{\text{kg/m}}^3\to {\text{g/cm}}^3=2700:1000{\text{g/cm}}^3=2.7{\text{g/cm}}^3 \\ m=\rho V \\ V=m/\rho =1400/2.7=\frac{14000}{27}\doteq 518.5185{\text{cm}}^3 \\ V=S_1\cdot h \\ {S}_1=V/h=518.5185/26=\frac{7000}{351}\doteq 19.943{\text{cm}}^2 \\ {S}_1=\pi r^2 \\ r=\sqrt{S_1/\pi }=\sqrt{19.943/3.1416}\doteq 2.5195\text{cm} \\ {S}_2=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 2.5195\cdot 26\doteq 411.5985{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 19.943+411.5985=451.4845{\text{cm}}^2 \end{gathered}$$

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