The surface

The surface of the cylinder is 1570 cm², its height is 15 cm. Find its volume and radius of the base.

Correct answer:

V =  4712.389 cm³
r =  10 cm

Step-by-step explanation:

$$\begin{gathered} S=1570{\text{cm}}^2 \\ h=15\text{ cm } \\ S=2\ast pi\ast r(r+h) \\ 1570=2\cdot 3.1415926\cdot r(r+15) \\ -6.2831851999999r^2-94.248r+1570=0 \\ 6.2831851999999r^2+94.248r-1570=0 \\ a=6.2831851999999;b=94.248;c=-1570 \\ D=b^2-4ac=94.248^2-4\cdot 6.2831851999999\cdot (-1570)=48341.046713937 \\ D>0 \\ {r}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-94.25\pm \sqrt{48341.05}}{12.5663704}} \\ {r}_{1,2}=-7.5\pm 17.496378622922 \\ {r}_1=9.9963786229224 \\ {r}_2=-24.996378622923 \\ \text{ Factored form of the equation: } \\ 6.2831851999999(r-9.9963786229224)(r+24.996378622923)=0 \\ r=[r_1]=[9.9964]=10\text{ cm } \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 10^2\cdot 15=4712.389{\text{cm}}^3 \end{gathered}$$

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