Question to test your Finding Limits Algebraically knowledge

Question

The radius of a right cylinder having a height of $15 ext{ cm}$ and a surface area of $U ext{ cm}^2$ is given as $r\left(U ight)=\frac15\left(\sqrt{225+\frac{5U}{\pi}}-15 ight)$ . Calculate ${\displaystyle\lim_{U o0^{+}}}r\left(U ight)$ and provide an interpretation.

Accepted Answer

$\frac15\sqrt{210}$ .

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 $\frac{1}{5} \sqrt{210}$ .

Answer

$\frac15\sqrt{210}$ .

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 $\frac{1}{5} \sqrt{210}$ .

Answer

$\frac15\sqrt{210}$ .

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 $\frac{1}{5} \sqrt{210}$ .

Answer

$\frac15\sqrt{210}$ .

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 $\frac{1}{5} \sqrt{210}$ .

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