KVPY SX SB Exam 2013 Question Paper

Question : 87 of 120

Marks: +1, -0

Suppose that the earth is a sphere of radius 6400 kilometers. The height from the earth’s surface from where exactly a fourth of the earth’s surface is visible, is

3200 km
$3200√2$ km
$3200√3$ km
6400 km

Validate

Solution:

AP = R sinθ
area of ring = (2π R sinθ). Rdθ
Total area required,

\π\R^2={|∫ ↖{θ}↙{0}2\π\R^2\sinθ\dθ|

1/2=1-\cos θ

\cos θ=1/2

Now

\cos θ=\R/{\R+\H}

1/2=\R/{\R+\H}=\R=\H=6400

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