Cylinder height

Calculate the height of the cylinder based on its surface S and the radius of the base r.
a) r = 2 cm, S = 120 cm square
b) r = 7 dm, S = 4,000 dm square
c) r = 0.2 m, S = 20 square meters

Final Answer:

a =  7.5493 cm
b =  83.9457 dm
c =  15.7155 m

Step-by-step explanation:

$$\begin{gathered} r_1=2 \\ {S}_1=120 \\ S=\pi r^2+2\pi rh \\ A=\pi \cdot r_1^2=3.1416\cdot 2^2\doteq 12.5664 \\ a=(S_1-2\cdot A)/(2\pi \cdot r_1)=(120-2\cdot 12.5664)/(2\cdot 3.1416\cdot 2)=7.5493\text{cm} \end{gathered}$$

$$\begin{gathered} r_2=7 \\ {S}_2=4000 \\ B=\pi \cdot r_2^2=3.1416\cdot 7^2\doteq 153.938 \\ b=(S_2-2\cdot B)/(2\pi \cdot r_2)=(4000-2\cdot 153.938)/(2\cdot 3.1416\cdot 7)=83.9457\text{dm} \end{gathered}$$

$$\begin{gathered} r_3=0.2 \\ {S}_3=20 \\ C=\pi \cdot r_3^2=3.1416\cdot 0.2^2\doteq 0.1257 \\ c=(S_3-2\cdot C)/(2\pi \cdot r_3)=(20-2\cdot 0.1257)/(2\cdot 3.1416\cdot 0.2)=15.7155\text{m} \end{gathered}$$

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