9000121003
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(BS_{DH}\)
and \(AE\), where
the point \(S_{DH}\) is the
center of the edge \(DH\).
\(70.53^{\circ }\)
\(29.47^{\circ }\)
\(35.26^{\circ }\)
\(54.74^{\circ }\)
A
9000117406
Level:
A
Determine whether the following planes are parallel, identical or intersecting.
\[\begin{aligned}
\rho \colon \frac{3}
{2}x -\frac{1}
{4}y + \frac{2}
{3}z -\frac{2}
{5} = 0,\qquad \sigma \colon \frac{2}
{3}x - 4y + \frac{3}
{2}z -\frac{5}
{2} = 0 & &
\end{aligned}\]
intersecting
identical
parallel, not identical
9000121004
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(S_{AE}S_{HC}\)
and \(S_{HC}S_{BF}\),
where \(S_{AE}\),
\(S_{HC}\) and
\(S_{BF}\) are the centers
of the segments \(AE\),
\(HC\) and
\(BF\),
respectively.
\(53.13^{\circ }\)
\(26.57^{\circ }\)
\(60^{\circ }\)
\(36.87^{\circ }\)
9000121001
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(AB\)
and \(AG\).
\(54.74^{\circ }\)
\(60^{\circ }\)
\(35.26^{\circ }\)
\(39.23^{\circ }\)
9000121005
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(AS_{BC}\)
and \(AD\), where
\(S_{BC}\) is the center
of the edge \(BC\).
\(63.43^{\circ }\)
\(26.57^{\circ }\)
\(53.13^{\circ }\)
\(36.87^{\circ }\)
9000121002
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(CD\)
and \(BH\).
\(54.74^{\circ }\)
\(60^{\circ }\)
\(35.26^{\circ }\)
\(39.23^{\circ }\)
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.
\(\left (96 + 140\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(600\, \mathrm{cm}^{2}\)
\(236\sqrt{5}\, \mathrm{cm}^{2}\)
\(\left (48 + 70\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(240\sqrt{5}\, \mathrm{cm}^{2}\)
9000121008
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(DB\)
and \(AG\).
\(90^{\circ }\)
\(45^{\circ }\)
\(35.26^{\circ }\)
\(53.13^{\circ }\)
9000120301
Level:
A
The length of a solid diagonal in a cube is
\(u = 2\sqrt{6}\, \mathrm{cm}\). Find
the surface area.
\(48\, \mathrm{cm}^{2}\)
\(24\, \mathrm{cm}^{2}\)
\(24\sqrt{2}\, \mathrm{cm}^{2}\)
\(16\sqrt{2}\, \mathrm{cm}^{2}\)
\(12\sqrt{6}\, \mathrm{cm}^{2}\)
9000121701
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(3\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(4\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
isosceles
equilateral
right
obtuse