Cylinder surface, volume

The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.

Correct answer:

S =  10367.26 cm²
V =  70685.83 cm³

Step-by-step explanation:

$$\begin{gathered} {\displaystyle \frac{S_1}{S_2}}={\displaystyle \frac{3}{5}} \\ {\displaystyle \frac{\pi r^2}{2\pi rh}}={\displaystyle \frac{3}{5}} \\ {\displaystyle \frac{r}{2h}}={\displaystyle \frac{3}{5}} \\ 5r=6h \\ h=r-5 \\ h=25cm \\ r=30cm \\ S=2\pi r^2+2\pi rh=2\pi \cdot 30\cdot (30+25)=10367.26{\text{cm}}^2 \end{gathered}$$

$V=\pi r^{2}h=\pi 30^2\cdot 25=70685.83{\text{cm}}^3$

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