1103163403
Level:
A
The length of a face diagonal of a cube is \( 6\sqrt2\,\mathrm{cm} \). Find the surface area of the cube.
\( 216\,\mathrm{cm}^2 \)
\( 36\,\mathrm{cm}^2 \)
\( 96\,\mathrm{cm}^2 \)
\( 72\sqrt2\,\mathrm{cm}^2 \)
Volume and surface area formulas
1103163405
Level:
A
The length of a space diagonal of a cube is \( 9\,\mathrm{cm} \). Find the volume of the cube.
\( 81\sqrt3\,\mathrm{cm}^3 \)
\( 9\sqrt3\,\mathrm{cm}^3 \)
\( 27\sqrt3\,\mathrm{cm}^3 \)
\( 81\,\mathrm{cm}^3 \)
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 \( 15\,\mathrm{cm} \).
\( V= 405\,\mathrm{cm}^3 \), \( S= 414\,\mathrm{cm}^2 \)
\( V= 414\,\mathrm{cm}^3 \), \( S= 405\,\mathrm{cm}^2 \)
\( V= 415\,\mathrm{cm}^3 \), \( S= 404\,\mathrm{cm}^2 \)
\( V= 42\,\mathrm{cm}^3 \), \( S= 84\,\mathrm{cm}^2 \)
9000120301
Level:
A
The length of a solid diagonal in a cube is
\(u = 2\sqrt{6}\, \mathrm{cm}\). Find
the surface area.
\(48\, \mathrm{cm}^{2}\)
\(24\, \mathrm{cm}^{2}\)
\(24\sqrt{2}\, \mathrm{cm}^{2}\)
\(16\sqrt{2}\, \mathrm{cm}^{2}\)
\(12\sqrt{6}\, \mathrm{cm}^{2}\)
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.
\(\left (96 + 140\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(600\, \mathrm{cm}^{2}\)
\(236\sqrt{5}\, \mathrm{cm}^{2}\)
\(\left (48 + 70\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(240\sqrt{5}\, \mathrm{cm}^{2}\)
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.
\(240\sqrt{5}\, \mathrm{cm}^{3}\)
\(900\, \mathrm{cm}^{3}\)
\(300\sqrt{5}\, \mathrm{cm}^{3}\)
\(600\sqrt{2}\, \mathrm{cm}^{3}\)
\(240\sqrt{2}\, \mathrm{cm}^{3}\)
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.
\(480\sqrt{3}\, \mathrm{cm}^{3}\)
\(960\, \mathrm{cm}^{3}\)
\(288\sqrt{3}\, \mathrm{cm}^{3}\)
\(160\sqrt{3}\, \mathrm{cm}^{3}\)
\(240\, \mathrm{cm}^{3}\)
1003165902
Level:
B
Find the capacity of a garden pool in the shape of a cylinder with the diameter of \( 366\,\mathrm{cm} \) and the height of \( 0.91\,\mathrm{m} \). Round your result to \( 2 \) decimal places.
\( 9.57\,\mathrm{m}^3 \)
\( 38.30\,\mathrm{m}^3 \)
\( 957.74\,\mathrm{m}^3 \)
\( 19.15\,\mathrm{m}^3 \)
1003165903
Level:
B
The volume of a cylinder with diameter of \( 20\,\mathrm{cm} \) is \( 5\,\mathrm{l} \). Find the height of the cylinder. Round your result to \( 2 \) decimal places.
\( 15.92\,\mathrm{cm} \)
\( 3.98\,\mathrm{cm} \)
\( 79.58\,\mathrm{cm} \)
\( 159.92\,\mathrm{cm} \)
1003165904
Level:
B
How many litres of water can a cylinder-shaped plastic barrel with diameter of \( 30.48\,\mathrm{cm} \) and height of \( 51\,\mathrm{cm} \) hold? Round your result to \( 1 \) decimal place.
\( 37.2\,\mathrm{l} \)
\( 148.9\,\mathrm{l} \)
\( 372.1\,\mathrm{l} \)
\( 62.3\,\mathrm{l} \)