9000121010
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(ES_{CG}\)
and \(AG\), where
\(S_{CG}\) is the center
of the \(CG\).
\(54.74^{\circ }\)
\(19.47^{\circ }\)
\(35.26^{\circ }\)
\(60^{\circ }\)
Metric Properties
9000120304
Level:
C
The side of a regular hexagonal prism
\(ABCDEFA'B'C'D'E'F'\) is
\(a = 3\, \mathrm{cm}\) and the height
\(v = 8\, \mathrm{cm}\). Find the length
of the diagonal \(AD'\).
\(10\, \mathrm{cm}\)
\(\sqrt{73}\, \mathrm{cm}\)
\(\sqrt{82}\, \mathrm{cm}\)
\(2\sqrt{8}\, \mathrm{cm}\)
\(2\sqrt{6}\, \mathrm{cm}\)
9000046408
Level:
B
Consider a cone of base radius \(r\)
and a special shape: the shape is such that the volume of the cone is related to the base radius
by the formula \(V =\pi r^{3}\).
Find the angle between the side of the cone and the base. Round your answer to two
decimal places.
\(71.57^{\circ }\)
\(45^{\circ }\)
\(63.43^{\circ }\)
9000045709
Level:
A
Let \(\omega \) be the
angle between the solid diagonal of a box and the base of this box. Find the expression which
allows to find \(\omega \).
\(\mathop{\mathrm{tg}}\nolimits \omega = \frac{\sqrt{2}}
{2} \)
\(\cos \omega = \frac{\sqrt{2}}
{2} \)
\(\sin \omega = \frac{\sqrt{2}}
{2} \)
\(\mathop{\mathrm{cotg}}\nolimits \omega = \frac{\sqrt{2}}
{2} \)
9000046407
Level:
A
Find the angle between the side of a cube and the cube’s space diagonal. Round the result to two decimal places.
\(35.26^{\circ }\)
\(45^{\circ }\)
\(54.76^{\circ }\)
9000046409
Level:
B
The base of a pyramid is a square with the side of \(2\, \mathrm{cm}\). The height of the pyramid is \(4\, \mathrm{cm}\). Find the angle between the lateral side of the pyramid and the base. Round your result to two decimal places.
\(75.96^{\circ }\)
\(70.52^{\circ }\)
\(79.98^{\circ }\)