Cylinder surface, volume

The area of the base and the area of the shell are in the ratio of 3:5. Its height is 5 cm less than the radius of the base. Calculate both surface area and volume.

Final Answer:

S =  10367.26 cm²
V =  70685.83 cm³

Step-by-step explanation:

$$\begin{gathered} S_1:S_2=3:5=3/5 \\ \frac{\pi r^2}{2\pi rh}=3:5 \\ r:2h=3:5 \\ 5r=6h \\ h=r-5 \\ 5\cdot r=6\cdot h \\ h=r-5 \\ 6h-5r=0 \\ h-r=-5 \\ Row2-\frac{1}{6}\cdot Row1\to Row2 \\ -0.17r=-5 \\ r=\frac{-5}{-0.16666667}=30 \\ h=\frac{0+5r}{6}=\frac{0+5\cdot 30}{6}=25 \\ h=25 \\ r=30 \\ {S}_1=\pi \cdot r^2=3.1416\cdot 30^2\doteq 2827.4334{\text{cm}}^2 \\ {S}_2=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 30\cdot 25\doteq 4712.389{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 2827.4334+4712.389=10367.26{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot h=2827.4334\cdot 25=70685.83{\text{cm}}^3$

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