The radius of a right cylinder having a height of $15\text{ cm}$ and a surface area of $U\text{ cm}^2$ is given as $r\left(U\right)=\frac15\left(\sqrt{225+\frac{5U}{\pi}}-15\right)$. Calculate ${\displaystyle\lim_{U\to0^{+}}}r\left(U\right)$ and provide an interpretation.

$\frac12\sqrt{105}$.

Interpretation: As U approaches 0 from the positive side, the radius of the cylinder approaches $\frac12\sqrt{105}$. This indicates that for a very small surface area, the radius of the cylinder will be approximately $\frac12\sqrt{105}$.

$\frac15\sqrt{21}$.

Interpretation: As U approaches 0 from the positive side, the radius of the cylinder approaches $\frac15\sqrt{21}$. This indicates that for a very small surface area, the radius of the cylinder will be approximately $\frac15\sqrt{21}$.

$\frac15\sqrt{210}$.

Interpretation: As U approaches 0 from the positive side, the radius of the cylinder approaches $\frac{1}{5} \sqrt{210}$. This indicates that for a very small surface area, the radius of the cylinder will be approximately $\frac{1}{5} \sqrt{210}$.

$\frac12\sqrt{210}$.

Interpretation: As U approaches 0 from the positive side, the radius of the cylinder approaches $\frac12\sqrt{210}$. This indicates that for a very small surface area, the radius of the cylinder will be approximately $\frac12\sqrt{210}$.