>A sphere of radius $7cm$ is put infront of light source at a distance of $15 m$ , what is area of "Illuminated" part of the sphere Today , i had a math contest and the following problem was of the problems :- > A sphere of radius $7cm$ is put infront of light source at a distance of $15 m$ , what is area of "Illuminated" part of the sphere > > a)$105$ square metres. > > b)$\frac{105}{11}$ square metres . > > c)$\frac{105}{22}$ square metres . > > c)$210$ square metres .

The illuminated part is a spherical cap, with area $$ S=2\pi R^2(1-\cos\theta). $$ In the case at hand it is easy to see that $$ \cos\theta={\hbox{sphere radius}\over\hbox{distance from sphere center to light source}}. $$ To get one of the listed results, we must take $15$ metres to be the distance from the light source to the sphere surface, so that $\cos\theta=7/22$ and $S=209.9155\ldots$ square metres ($S=210$ if we take $\pi=22/7$).