Cylindrical tank

A tank has the shape of a cylinder with a diameter of 1.6 m and a length of 4.5 m.
At least how many cylindrical barrels with a diameter of 0.8 m and a height of 1.5 m are needed to empty a tank?

Correct answer:

n =  12

Step-by-step explanation:

$$\begin{gathered} D_1=0.8\text{m} \\ {h}_1=1.5\text{m} \\ {D}_2=1.6\text{m} \\ {h}_2=4.5\text{m} \\ {V}_1=\pi \cdot (D_1/2{)}^2\cdot h_1=3.1416\cdot (0.8/2{)}^2\cdot 1.5\doteq 0.754{\text{m}}^3 \\ {V}_2=\pi \cdot (D_2/2{)}^2\cdot h_2=3.1416\cdot (1.6/2{)}^2\cdot 4.5\doteq 9.0478{\text{m}}^3 \\ N=V_2/V_1=9.0478/0.754=12 \\ n=\lceil N\rceil =\lceil 12\rceil =12 \\ \text{ Verifying Solution: } \\ {n}_2=\frac{h_2}{h_1}\cdot \frac{D_2^2}{D_1^2}=\frac{4.5}{1.5}\cdot \frac{1.6^2}{0.8^2}=12 \end{gathered}$$

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