Volume and surface of solids

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.
\( 12\sqrt3\,\mathrm{cm}^3 \)
\( 12\sqrt2\,\mathrm{cm}^3 \)
\( 24\sqrt3\,\mathrm{cm}^3 \)
\( 36\sqrt2\,\mathrm{cm}^3 \)

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.
\( 8\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)
\( 12\,\mathrm{cm} \)
\( 8\sqrt3\,\mathrm{cm} \)

2000003301

Level: 
B
The axial section of a cylinder is a square with the diagonal length of \( 5\sqrt{2}\,\mathrm{cm} \). The lateral surface area of the cylinder is equal to:
\( 25\pi\,\mathrm{cm}^2 \)
\( 25\,\mathrm{cm}^2 \)
\( 25\sqrt{2}\,\mathrm{cm}^2 \)
\( 25\sqrt{2}\pi\,\mathrm{cm}^2 \)

2000003303

Level: 
B
The volume of a regular quadrilateral pyramid is \( 432\,\mathrm{cm} ^3\) and the base edge of the pyramid has the length equal to \( 12\,\mathrm{cm} \). The height of the pyramid is:
\( 9\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( 36\,\mathrm{cm} \)
\( 27\,\mathrm{cm} \)

2000003306

Level: 
B
A rectangle with the sides of \( 4\,\mathrm{cm} \) and \( 6\,\mathrm{cm} \) is rotated around its longer side thus giving rise to a solid. Find the volume of such a solid?
\( 96\pi\,\mathrm{cm}^3 \)
\( 48\pi\,\mathrm{cm}^3 \)
\( 96\,\mathrm{cm}^3 \)
\( 144\pi\,\mathrm{cm}^3 \)

2010016502

Level: 
B
The base of a triangular pyramid is an equilateral triangle with a side of \( 8\,\mathrm{cm} \) (see the picture). The volume of the pyramid is \( 16\sqrt3\,\mathrm{cm}^3 \). Find the perpendicular height of the pyramid.
\( 3\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
\( 6\,\mathrm{cm} \)
\( 3\sqrt3\,\mathrm{cm} \)