Juice-soaked 17173

1. Find the dimensions of a 5-liter cylindrical container if the height of the container is equal to the radius of the base.

2. There is three dl of juice in a cylindrical glass with an inner diameter of 8 cm. Calculate the area of ​​the juice-soaked portion of the glass.

3. The can of cucumbers is cylindrical. Its height is 13 cm, and the diameter of the base is 12 cm. After filling with cucumbers, another two dl of infusion could be poured into it. Calculate the volume of canned cucumbers.

Correct answer:

r₁ =  1.1675 dm
h₁ =  1.1675 dm
S₂ =  200.2655 cm²
V₃ =  1270.2654 cm³

Step-by-step explanation:

$$\begin{gathered} V=5\text{l} \\ 1l=1d{m}^3 \\ {h}_1=r_1 \\ V=\pi r_1^2{h}_1=\pi r_1{}^3 \\ {r}_1=\sqrt[3]{V/\pi }=\sqrt[3]{5/3.1416}=1.1675\text{dm} \end{gathered}$$

$h_1=r_1=1.1675=1.1675\text{dm}$

$$\begin{gathered} D=8\text{cm} \\ V=3\text{dl}\to {\text{cm}}^3=3\cdot 100{\text{cm}}^3=300{\text{cm}}^3 \\ r=D/2=8/2=4\text{cm} \\ Sp=\pi \cdot r^2=3.1416\cdot 4^2\doteq 50.2655{\text{cm}}^2 \\ V=Sp\cdot h_2 \\ {h}_2=V/Sp=300/50.2655\doteq 5.9683\text{cm} \\ {S}_2=\pi \cdot D\cdot h_2+Sp=3.1416\cdot 8\cdot 5.9683+50.2655=200.2655{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} h_3=13\text{cm} \\ {D}_3=12\text{cm} \\ Vu=2\text{dl}\to {\text{cm}}^3=2\cdot 100{\text{cm}}^3=200{\text{cm}}^3 \\ {r}_3=D_3/2=12/2=6\text{cm} \\ {V}_{33}=\pi \cdot r_3^2\cdot h_3=3.1416\cdot 6^2\cdot 13\doteq 1470.2654{\text{cm}}^3 \\ {V}_3=V_{33}-Vu=1470.2654-200=1270.2654{\text{cm}}^3 \end{gathered}$$

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