Q.

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

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a

4012π

b

none of these

c

3992π

d

4002π

answer is A.

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Detailed 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=2h

Let h=20 and h+Δh=20.025Δh=0.025

Let S be the lateral surface. Then,

S=2πh2                                             [S=πrlS=πh×2h]dSdh=22πh dSdhh=20=402π ΔS=dSdhΔhΔS=402π×0.025=2π

Also, at h=20, we have S=4002π

 S+ΔS=4002π+2π=4012π

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