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A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will
For a point source,
Intensity varies as
$$I\propto\frac{1}{r^2}$$
If volume of spherical detector increases 8 times,
$$V'=8V$$
For sphere,
$$V=\frac{4}{3}\pi r^3$$
so
$$r'^3=8r^3$$
$$r'=2r$$
Now intensity becomes
$$I'=\frac{1}{(2r)^2}$$
$$=\frac{1}{4}\cdot\frac{1}{r^2}$$
So
$$I'=\frac{I}{4}$$
Hence intensity becomes one-fourth of original.
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