The semi-vertical angle of a cone is 45°. If the height of the cone is 20.025, then its approximate lateral surface area, is

# The semi-vertical angle of a cone is 45°. If the height of the cone is 20.025, then its approximate lateral surface area, is

1. A

$401\sqrt{2}\pi$

2. B

$400\sqrt{2}\pi$

3. C

$399\sqrt{2}\pi$

4. D

none of these

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### Solution:

Let $r$ be the radius, $h$ be the height and $I$ be the slant

height of a cone of semi-vertical angle 45°. Then,

$r=h$ and $I=\sqrt{2h}$

Let

Let $S$ be the lateral surface. Then,

Also, at $h=20,$ we have $S=400\sqrt{2\mathrm{\pi }}$

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