Volume and surface of solids

1003163704

Level: 
A
A rectangular aquarium has length of \( 50\,\mathrm{cm} \) and width of \( 30\,\mathrm{cm} \). Suppose we place a decorative stone in the aquarium and the water level rises by \( 4\,\mathrm{cm} \). What is the volume of the stone?
\( 6\,\mathrm{dm}^3 \)
\( 60\,\mathrm{dm}^3 \)
\( 1.5\,\mathrm{dm}^3 \)
\( 150\,\mathrm{dm}^3 \)

1003163701

Level: 
A
Find the volume and the surface area of a rectangular prism with the edges of lengths \( 8\,\mathrm{cm} \), \( 6\,\mathrm{cm} \), and \( 4\,\mathrm{cm} \).
\( V= 192\,\mathrm{cm}^3 \), \( S= 208\,\mathrm{cm}^2 \)
\( V= 192\,\mathrm{cm}^3 \), \( S= 104\,\mathrm{cm}^2 \)
\( V= 208\,\mathrm{cm}^3 \), \( S= 192\,\mathrm{cm}^2 \)
\( V= 192\,\mathrm{cm}^3 \), \( S= 416\,\mathrm{cm}^2 \)

9000120310

Level: 
A
The base of a rectangular box \(ABCDEFGH\) has sides \(|AB| = 6\, \mathrm{cm}\) and \(|BC| = 8\, \mathrm{cm}\). The angle between the solid diagonal \(AG\) and the base \(ABC\) is \(60^{\circ }\). Find the volume of the box.
\(480\sqrt{3}\, \mathrm{cm}^{3}\)
\(960\, \mathrm{cm}^{3}\)
\(288\sqrt{3}\, \mathrm{cm}^{3}\)
\(160\sqrt{3}\, \mathrm{cm}^{3}\)
\(240\, \mathrm{cm}^{3}\)

9000120307

Level: 
A
The lengths of a side, base diagonal and solid diagonal through the vertex \(A\) in a rectangular box \(ABCDEFGH\) are \(|AB| = 6\, \mathrm{cm}\), \(|AC| = 10\, \mathrm{cm}\), \(|AG| = 15\, \mathrm{cm}\). Find the volume of the box.
\(240\sqrt{5}\, \mathrm{cm}^{3}\)
\(900\, \mathrm{cm}^{3}\)
\(300\sqrt{5}\, \mathrm{cm}^{3}\)
\(600\sqrt{2}\, \mathrm{cm}^{3}\)
\(240\sqrt{2}\, \mathrm{cm}^{3}\)

9000120308

Level: 
C
The height \(v\) of a regular hexagonal prism is a double of its side \(a\). The volume of the prism is \(648\sqrt{3}\, \mathrm{cm}^{3}\). Use this information to find the length of the longest solid diagonal in the prism.
\(12\sqrt{2}\, \mathrm{cm}\)
\(10\sqrt{6}\, \mathrm{cm}\)
\(12\sqrt{6}\, \mathrm{cm}\)
\(6\sqrt{10}\, \mathrm{cm}\)
\(\sqrt{432}\, \mathrm{cm}\)

9000120306

Level: 
A
The lengths of a side, face diagonal and solid diagonal through the vertex \(A\) in a rectangular box \(ABCDEFGH\) are \(|AB| = 6\, \mathrm{cm}\), \(|AC| = 10\, \mathrm{cm}\), \(|AG| = 15\, \mathrm{cm}\). Find the surface area.
\(\left (96 + 140\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(600\, \mathrm{cm}^{2}\)
\(236\sqrt{5}\, \mathrm{cm}^{2}\)
\(\left (48 + 70\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(240\sqrt{5}\, \mathrm{cm}^{2}\)