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AP EAMCET · Maths · Application of Derivatives

The semi-vertical angle of a right circular cone is \(45^{\circ}\). If the radius of the base of the cone is measured as 14 cm with an error of \(\left(\frac{\sqrt{2}-1}{11}\right) \mathrm{cm}\), then the approximate error in measuring its total surface area is (in sq. cm )

  1. A \(14\)
  2. B \(8\)
  3. C \(5\)
  4. D \(3\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(8\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \quad \alpha=45^{\circ}, r=14 \mathrm{~cm}, l=\frac{r}{\sin 45^{\circ}}=14 \sqrt{2} \\ & \text { Total surface area }(\mathrm{A})=\pi \mathrm{r}(\mathrm{r}+l) \\ & \mathrm{A}=\pi r^2(1+\sqrt{2}) \\ & \frac{d \mathrm{~A}}{d r}=2 \pi r(1+\sqrt{2}) \\ & d A=2 \pi…