Volume and surface of solids

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 \( 8\,\mathrm{cm} \).
\( 12\left(3+\sqrt{73}\right)\,\mathrm{cm}^2 \)
\( 132\,\mathrm{cm}^2 \)
\( 156\,\mathrm{cm}^2 \)
\( 12\left(3+2\sqrt{73}\right)\,\mathrm{cm}^2 \)

1003163809

Level: 
A
The meteo stats show that during the last storm there was a rainfall of \( 5\,\mathrm{mm} \). How much water rained down on a rectangular garden sized \( 10\,\mathrm{m} \) by \( 7\,\mathrm{m} \)?
\( 350\,\mathrm{l} \)
\( 0.35\,\mathrm{l} \)
\( 3.50\,\mathrm{l} \)
\( 35\,\mathrm{l} \)

1003163808

Level: 
A
A rectangular pool is filled with water \( 120\,\mathrm{cm} \) deep. The volume of water in the pool is \( 24\,\mathrm{m}^3 \). Find the dimensions of the pool bottom, if you know that its length is by \( 1\,\mathrm{m} \) larger than its width.
\( 5\,\mathrm{m} \), \( 4\,\mathrm{m} \)
\( 4\,\mathrm{m} \), \( 3\,\mathrm{m} \)
\( 6\,\mathrm{m} \), \( 5\,\mathrm{m} \)
\( 3.5\,\mathrm{m} \), \( 4.5\,\mathrm{m} \)

1003163807

Level: 
A
A rectangular prism has edges of the lengths of \( 2\,\mathrm{dm} \), \( 4\,\mathrm{dm} \) and \( 5\,\mathrm{dm} \). What is the maximum number of cubes with the edge length of \( 5\,\mathrm{cm} \) that can fit into this prism?
\( 320 \)
\( 1600 \)
\( 32 \)
\( 160 \)

1003163806

Level: 
A
Dimensions of a rectangular prism are in ratio \( 3:4:7 \) and the volume of the prism is \( 672\,\mathrm{cm}^3 \). Find the length of its longest side diagonal.
\( 2\sqrt{65}\,\mathrm{cm} \)
\( 13\sqrt{10}\,\mathrm{cm} \)
\( 4\sqrt{65}\,\mathrm{cm} \)
\( 260\,\mathrm{cm} \)