Ivan Shishkin, Rye (1878)

Problems/GeometryUnreviewed

Partial solar eclipse

by Ancient Tree·
9
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The Moon passes in front of the Sun. As seen from Earth, the apparent diameter of the Moon is exactly equal to the apparent radius of the Sun.

image

What proportion of the Sun is blocked?

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Solution by Ancient Tree

Discussions1 useful vote

Denoting the radius of the Sun as RR, and the radius of the Moon as rr, we have that R=2rR=2r.
Therefore, the area of the Moon is πr2\pi r^{2}, while the area of the Sun is πR2=π(2r)2=π×4r2=4πr2\pi R^{2}=\pi (2r)^{2}=\pi\times 4r^{2}=4\pi r^{2}.

That is, the area of the Sun is 4 times bigger !
So one quarter of the Sun is blocked at this moment of the eclipse.

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