Refer to the diagram shown below from page 2 of the textbook. A plane angle \( d\theta \) is defined as \( d\theta = \frac{ds}{r} \) and a solid angle \( d\Omega \) as \( d\Omega = \frac{dA}{r^2} \). If a spherical surface of radius \( r = 2.0\text{ m} \) has a cap of surface area \( dA = 0.8\text{ m}^2 \), what is the solid angle subtended by this cap at the center of the sphere?

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Correct answer · Option A

\( 0.2\text{ sr} \)

Solid angle \( d\Omega = \frac{dA}{r^2} = \frac{0.8}{(2.0)^2} = \frac{0.8}{4.0} = 0.2\text{ sr} \).