Cylinder shell volume

The cylinder has a shell surface of 88 square cm and a volume of 176 cubic cm. Calculate the radius, height, and surface area of the given solid.

Final Answer:

r =  4 cm
h =  3.5014 cm
S₂ =  188.531 cm²

Step-by-step explanation:

$$\begin{gathered} S=88{\text{cm}}^2 \\ V=176{\text{cm}}^3 \\ V=\pi r^{2}h=S_1\cdot h \\ S=2\pi \cdot r\cdot h \\ h=\frac{S}{2\pi \cdot r} \\ V=\pi r^2\frac{S}{2\pi \cdot r} \\ V=\frac{r\cdot S}{2} \\ r=2\cdot V/S=2\cdot 176/88=4\text{cm} \\ h=\frac{S}{2\pi \cdot r}=\frac{88}{2\cdot 3.1416\cdot 4}\doteq 3.5014\text{cm} \end{gathered}$$

$$\begin{gathered} S_1=\pi \cdot r^2=3.1416\cdot 4^2\doteq 50.2655{\text{cm}}^2 \\ {S}_2=S+2\cdot S_1=88+2\cdot 50.2655\doteq 188.531{\text{cm}}^2 \\ \text{ Verifying Solution: } \\ {S}_9=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 4\cdot 3.5014=88{\text{cm}}^2 \\ {V}_9=\pi \cdot r^2\cdot h=3.1416\cdot 4^2\cdot 3.5014=176{\text{cm}}^3 \\ {S}_9=S,V_9=V \end{gathered}$$

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