Question

An opaque sphere of radius R lies on a horizontal plane. On the perpendicular through the point of contact there is a point source of light a distance R above the sphere then area of shadow on the plane is

• A. $\pi R^2$
• B. $2\pi R^2$
• C. $3\pi R^2$
• D. $27\pi R^2$

Answer 1

The correct option is C $3\pi R^2$


$sin\theta =\frac{R}{2R}\Rightarrow \theta ={30}^{\circ }$

$tan\theta =\frac{r}{3R}$

$r=\sqrt{3}R\Rightarrow Area=\pi r^2=3\pi R^2$