Diameter = height

The cylinder's surface, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.

Correct answer:

V =  21189.6268 cm³

Step-by-step explanation:

$$\begin{gathered} S=4239{\text{cm}}^2 \\ D=h=2r \\ S=2\pi r^2+2\pi rh=2\pi r(r+h) \\ S=2\pi r(r+2r)=2\pi r3r=6\pi r^2 \\ r=\sqrt{{\displaystyle \frac{S}{6\pi }}}=\sqrt{{\displaystyle \frac{4239}{6\cdot 3.1416}}}\doteq 14.9962\text{ cm } \\ h=2\cdot r=2\cdot 14.9962\doteq 29.9924\text{ cm } \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 14.9962^2\cdot 29.9924=21189.6268{\text{cm}}^3=2.119\cdot 10^4{\text{cm}}^3 \end{gathered}$$

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