Answer:
Diameter of smallest circular opening = 12.81 in
Step-by-step explanation:
Given:-
Width of rectangular box(W)=10 in.
Length of rectangular box(L)=8 in.
Height of rectangular box(H)=10 in.
For box to fit in the smallest circular opening we need to find the diagonal of the rectangular box, therefore
diagonal of rectangular box=diameter of smallest circular opening
So,
[tex]Diagonal\ (d)=\sqrt{width^{2}+length^{2} }[/tex]
[tex]d=\sqrt{W^{2} +L^{2} }[/tex]
[tex]d=\sqrt{10^{2}+8^{2}}[/tex]
[tex]d=\sqrt{100+64}[/tex]
[tex]d=\sqrt{164}[/tex]
[tex]d=12.81\ in.[/tex]
[tex]\therefore\ diagonal\ (d)=12.81\ in[/tex]
Therefore diameter of smallest circular opening = 12.81 in.
