Height as diameter of base

The rotary cylinder has a height equal to the base diameter and a surface of 471 cm². Calculate the volume of a cylinder.

Correct answer:

V =  784.801 cm³

Step-by-step explanation:

$$\begin{gathered} S=471{\text{cm}}^2 \\ h=D \\ h=2r \\ S=2\pi r^2+2\pi rh \\ S=2\pi r^2+4\pi r^2 \\ S=6\pi r^2 \\ r=\sqrt{S\mathrm{/}(6\pi )}=\sqrt{471\mathrm{/}(6\cdot 3.1416)}\doteq 4.9987\text{ cm } \\ h=2\cdot r=2\cdot 4.9987\doteq 9.9975\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 4.9987^2={\displaystyle \frac{157}{2}}=78.5{\text{cm}}^2 \\ {S}_2=2\cdot S_1+2\pi \cdot r\cdot h=2\cdot 78.5+2\cdot 3.1416\cdot 4.9987\cdot 9.9975=471{\text{cm}}^2 \\ {S}_2=S \\ V=S_1\cdot h=78.5\cdot 9.9975=784.801{\text{cm}}^3 \end{gathered}$$

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