Since, the dimensions of sandbox are [tex]t^2[/tex] meter, [tex]t^5[/tex] meter and [tex]3v^2[/tex] meter.
One cubic meter of the sandbox contains [tex]3s^{21}[/tex] grains of sand.
We have to determine the grains of sand are in the sandbox.
So, let us determine the volume of the sandbox.
Since, sandbox is in shape of rectangular prism.
Therefore, Volume of sandbox = [tex]l \times b \times h[/tex]
= [tex]t^2 \times t^5 \times 3v^2[/tex]
= [tex]3t^7 v^2[/tex] cubic meters.
Since, one cubic meter of the sandbox contains [tex]3s^{21}[/tex] grains of sand.
Therefore, Number of grains in the sandbox = [tex]3t^7 v^2 \times 3s^{21}[/tex]
= [tex]9v^2 s^{21} t^7[/tex]
Option D is the correct answer.
