A

1103056006

Level: 
A
The cube \( ABCDEFGH \) shown in the picture has edges of length \( a=6\,\mathrm{cm} \). Find the distance between the point \( B \) and the line \( EG \).
\( 3\sqrt6\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)
\( 3\sqrt5\,\mathrm{cm} \)
\( \frac{3\sqrt6}2\,\mathrm{cm} \)

1103056004

Level: 
A
The cube \( ABCDEFGH \) shown in the picture has edges of length \( a=6\,\mathrm{cm} \). Let \( S_1 \) be the midpoint of the diagonal \( ED \) and let \( S_2 \) be the midpoint of the diagonal \( CH \). Find the distance between the points \( S_1 \) and \( S_2 \).
\( 3\sqrt2\,\mathrm{cm} \)
\( 6\sqrt2\,\mathrm{cm} \)
\( \sqrt2\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)

1103056003

Level: 
A
The cube \( ABCDEFGH \) shown in the picture has edges of length \( a=6\,\mathrm{cm} \). Let \( S \) be the midpoint of the edge \( FG \). Find the distance between the points \( E \) and \( S \).
\( 3\sqrt5\,\mathrm{cm} \)
\( 6\sqrt5\,\mathrm{cm} \)
\( \sqrt5\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)

1103056002

Level: 
A
The cube \( ABCDEFGH \) shown in the picture has edges of length \( a=6\,\mathrm{cm} \). Let \( S \) be the midpoint of the base \( ABCD \). Find the distance between the points \( H \) and \( S \).
\( 3\sqrt6\,\mathrm{cm} \)
\( 6\sqrt5\,\mathrm{cm} \)
\( 3\sqrt5\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)