Volume and surface of solids

2010016506

Level: 
B
The volume of a right circular cone is \(96\pi\,\mathrm{cm}^3\) and its diameter and the perpendicular height are in the ratio \(3:2\). Find the surface \(S\) of the cone.
\( S=96\pi\,\mathrm{cm}^2 \)
\( S=60\pi\,\mathrm{cm}^2 \)
\( S=96\,\mathrm{cm}^2 \)
\( S=60\,\mathrm{cm}^2 \)

2010016504

Level: 
B
How much paper do we need to label the can of peaches with diameter of \( 12\,\mathrm{cm} \) and height of \( 18\,\mathrm{cm} \)? (Label covers the side of the can completely, the bottom and the top base are not labelled.) Round your result to \( 1 \) decimal place.
\( 678.6\,\mathrm{cm}^2 \)
\( 1357.1\,\mathrm{cm}^2 \)
\( 339.3\,\mathrm{cm}^2 \)
\( 904.8\,\mathrm{cm}^2 \)

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.
\( 3\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
\( 6\,\mathrm{cm} \)
\( 3\sqrt3\,\mathrm{cm} \)

2010016501

Level: 
A
Find the volume and the surface area of a rectangular prism with the edges of lengths \( 3\,\mathrm{cm} \), \( 9\,\mathrm{cm} \) and \( 15\,\mathrm{cm} \).
\( V= 405\,\mathrm{cm}^3 \), \( S= 414\,\mathrm{cm}^2 \)
\( V= 414\,\mathrm{cm}^3 \), \( S= 405\,\mathrm{cm}^2 \)
\( V= 415\,\mathrm{cm}^3 \), \( S= 404\,\mathrm{cm}^2 \)
\( V= 42\,\mathrm{cm}^3 \), \( S= 84\,\mathrm{cm}^2 \)

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?
\( 96\pi\,\mathrm{cm}^3 \)
\( 48\pi\,\mathrm{cm}^3 \)
\( 96\,\mathrm{cm}^3 \)
\( 144\pi\,\mathrm{cm}^3 \)

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:
\( 9\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( 36\,\mathrm{cm} \)
\( 27\,\mathrm{cm} \)