Lines and planes: distances and angles

1103107002

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the lines \( A'D' \) and \( C'D' \) (see the picture).
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 72^{\circ} \)
\( 54.7^{\circ} \)

1103107003

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the lines \( A'D' \) and \( CC' \) (see the picture).
\( 90^{\circ} \)
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 72^{\circ} \)

1103107004

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the plane \( ABB' \) and the plane \( AEE' \) (see the picture).
\( 90^{\circ} \)
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 72^{\circ} \)

1103107005

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the plane \( ADD' \) and the plane \( AEE' \) (see the picture).
\( 30^{\circ} \)
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 22.5^{\circ} \)

1103107006

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 4\sqrt6\,\mathrm{cm} \). Find the distance between the lines \( FA \) and \( C'D' \) (see the picture).
\( 12\,\mathrm{cm} \)
\( 8\sqrt3\,\mathrm{cm} \)
\( 4\sqrt6\,\mathrm{cm} \)
\( 10\,\mathrm{cm} \)

1103107007

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 6\,\mathrm{cm} \). Find the distance between the lines \( FA \) and \( E'B' \) (see the picture).
\( 4\sqrt3\,\mathrm{cm} \)
\( 2\sqrt{13}\,\mathrm{cm} \)
\( 2\sqrt{10}\,\mathrm{cm} \)
\( 2\sqrt3\,\mathrm{cm} \)

1103107008

Level: 
C
A regular hexagonal prism \( ABCDEFA'B'C'D'E'F' \) has the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 6\,\mathrm{cm} \). Let \( S \) be the middle of the top face \( A'B'C'D'E'F' \). Find the distance between the point \( S \) and the line \( BC \) (see the picture).
\( 4\sqrt3\,\mathrm{cm} \)
\( 2\sqrt{13}\,\mathrm{cm} \)
\( 2\sqrt{21}\,\mathrm{cm} \)
\( 4\sqrt{21}\,\mathrm{cm} \)

1103107009

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the distance between the points \( F' \) and \( C \) (see the picture).
\( 8\sqrt2\,\mathrm{cm} \)
\( 4\sqrt5\,\mathrm{cm} \)
\( 4\sqrt7\,\mathrm{cm} \)
\( 4\sqrt2\,\mathrm{cm} \)

1103107010

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the distance between the points \( E' \) and \( C \) (see the picture).
\( 4\sqrt7\,\mathrm{cm} \)
\( 8\sqrt2\,\mathrm{cm} \)
\( 8+4\sqrt3\,\mathrm{cm} \)
\( 16\sqrt7\,\mathrm{cm} \)

1103107011

Level: 
C
Let \( ABCDEFA'B'C'D'E'F' \) be a regular hexagonal prism with the base edge length of \( 4\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \). Find the angle between the line \( FC' \) and the base plane \( ABC \) (see the picture).
\( 45^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)
\( 72^{\circ} \)