Metric properties

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).
\( 4\sqrt3\,\mathrm{cm} \)
\( 2\sqrt{13}\,\mathrm{cm} \)
\( 2\sqrt{10}\,\mathrm{cm} \)
\( 2\sqrt3\,\mathrm{cm} \)

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).
\( 12\,\mathrm{cm} \)
\( 8\sqrt3\,\mathrm{cm} \)
\( 4\sqrt6\,\mathrm{cm} \)
\( 10\,\mathrm{cm} \)

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).
\( 30^{\circ} \)
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 22.5^{\circ} \)

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).
\( 90^{\circ} \)
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 72^{\circ} \)

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).
\( 90^{\circ} \)
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 72^{\circ} \)

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).
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 72^{\circ} \)
\( 54.7^{\circ} \)

1103107001

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 \( FC' \) and \( CF' \) (see the picture).
\( 90^{\circ} \)
\( 45^{\circ} \)
\( 60^{\circ} \)
\( 72^{\circ} \)

1103061408

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=|BC|=6\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the planes \( ABC \) and \( AFH \) (see the picture). Round the result to two decimal places.
\( 62.06^{\circ} \)
\( 53.13^{\circ} \)
\( 45^{\circ} \)
\( 60^{\circ} \)

1103061407

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( CG \) and \( EC \) (see the picture). Round the result to two decimal places.
\( 42.03^{\circ} \)
\( 47.97^{\circ} \)
\( 45^{\circ} \)
\( 50.04^{\circ} \)

1103061406

Level: 
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the planes \( ABC \) and \( EFC \) (see the picture). Round the result to two decimal places.
\( 63.43^{\circ} \)
\( 26.57^{\circ} \)
\( 45^{\circ} \)
\( 56.2^{\circ} \)