1103162501
Level:
B
Let a square \( ABCD \) be translated by vector \( \overrightarrow{AC} \). From the pictures below choose the one that shows correctly the translation \( A'B'C'D' \) of the square \( ABCD \).
B
1103189208
Level:
B
The base of a triangular pyramid is an equilateral triangle with a side of \( 6\,\mathrm{cm} \) (see the picture). The volume of the pyramid is \( 24\sqrt3\,\mathrm{cm}^3 \). Find the perpendicular height of the pyramid.
\( 8\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)
\( 12\,\mathrm{cm} \)
\( 8\sqrt3\,\mathrm{cm} \)
1103189207
Level:
B
The base of a triangular pyramid is an equilateral triangle with a side of \( 6\,\mathrm{cm} \) (see the picture). The height of the pyramid is \( 4\,\mathrm{cm} \). Find the volume of the pyramid.
\( 12\sqrt3\,\mathrm{cm}^3 \)
\( 12\sqrt2\,\mathrm{cm}^3 \)
\( 24\sqrt3\,\mathrm{cm}^3 \)
\( 36\sqrt2\,\mathrm{cm}^3 \)
1103189206
Level:
B
The edge length of the regular tetrahedron shown in the picture is \( 6\,\mathrm{cm} \). Find the surface area of this tetrahedron.
\( 36\sqrt3\,\mathrm{cm}^2 \)
\( 12\sqrt3\,\mathrm{cm}^2 \)
\( 36\sqrt6\,\mathrm{cm}^2 \)
\( 9\sqrt3\,\mathrm{cm}^2 \)
1103189205
Level:
B
The edge length of the regular tetrahedron shown in the picture is \( 6\,\mathrm{cm} \). Find the height of this tetrahedron.
\( 2\sqrt6\,\mathrm{cm} \)
\( 6\sqrt6\,\mathrm{cm} \)
\( 3\sqrt3\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)
1103189204
Level:
B
The edge length of the regular tetrahedron shown in the picture is \( 6\,\mathrm{cm} \). Find the volume of this tetrahedron.
\( 18\sqrt2\,\mathrm{cm}^3 \)
\( 36\sqrt2\,\mathrm{cm}^3 \)
\( 18\sqrt3\,\mathrm{cm}^3 \)
\( 54\sqrt2\,\mathrm{cm}^3 \)
1103189203
Level:
B
Find the volume of a square pyramid (see the picture) with the base edge length of \( 6\,\mathrm{cm} \) and the slant height of \( 5\,\mathrm{cm} \).
\( 48\,\mathrm{cm}^3 \)
\( 144\,\mathrm{cm}^3 \)
\( 60\,\mathrm{cm}^3 \)
\( 180\,\mathrm{cm}^3 \)
1103189202
Level:
B
Find the surface area of a square pyramid (see the picture) with the base edge length of \( 6\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \).
\( 12\left(3+\sqrt{73}\right)\,\mathrm{cm}^2 \)
\( 132\,\mathrm{cm}^2 \)
\( 156\,\mathrm{cm}^2 \)
\( 12\left(3+2\sqrt{73}\right)\,\mathrm{cm}^2 \)
1103189201
Level:
B
Find the volume of a square pyramid (see the picture) with the base edge length of \( 6\,\mathrm{cm} \) and the height of \( 8\,\mathrm{cm} \).
\( 96\,\mathrm{cm}^3 \)
\( 288\,\mathrm{cm}^3 \)
\( 768\,\mathrm{cm}^3 \)
\( 128\,\mathrm{cm}^3 \)
1003077113
Level:
B
The curved surface of a cone has an area of \( 4.15\,\mathrm{cm}^2 \). If we flatten it into a plain, we get a sector of a circle with the central angle of \( 126^{\circ} \). Calculate the volume of this cone. Round the result to two decimal places.
\( 0.88\,\mathrm{cm}^3 \)
\( 0.62\,\mathrm{cm}^3 \)
\( 0.15\,\mathrm{cm}^3 \)
\( 311.00\,\mathrm{cm}^3 \)