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.

Correct answer:

S =  10367.26 cm²
V =  70685.83 cm³

Step-by-step explanation:

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

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

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