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AP EAMCET · Maths · Heights and Distances

The semivertical angle of a cone is \(45^{\circ}\). If the height of the cone is \(20.025 \mathrm{~cm}\), then the approximate value of its lateral surface area (in sq. \(\mathrm{cm}\) ) is

  1. A \(401 \sqrt{2} \pi\)
  2. B \(400 \sqrt{2} \pi\)
  3. C \(402 \sqrt{2} \pi\)
  4. D \(405 \sqrt{2} \pi\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(401 \sqrt{2} \pi\)

Step-by-step Solution

Detailed explanation

In \(\triangle A O B\), \(\begin{aligned} & \tan 45^{\circ}=\frac{r}{h} \\ & 1=\frac{r}{h} \Rightarrow r=h \end{aligned}\) and \(l^2=r^2+h^2\) \(\begin{aligned} & l=\sqrt{h^2+h^2} \\ & l=\sqrt{2 h^2}=\sqrt{2} h \end{aligned}\) \([\because r=h]\) Lateral surface area…