1103162605
Level:
C
Let \(ABC\) be a triangle (see the picture). Find the dilated image of the triangle with \( O \) (the origin) being the centre of dilation and the scale factor \( 2 \).
C
1103162604
Level:
C
Let \( ABC\) be a triangle with the centroid \( T \) (see the picture). Find the dilated image of the triangle with \( T \) being the centre of dilation and the scale factor \( -\frac12 \).
1103162603
Level:
C
Let \( ABC \) be a triangle (see the picture). Find the dilated image of the triangle with \( A \) being the centre of dilation and the scale factor \( \frac54 \).
1103162602
Level:
C
Let \( ABCD \) be a square. Find the dilated image of the square with \( S \) being the centre of dilation and scale factor \( -\frac12 \). The point \( S \) is also the middle of the square \( ABCD \) (see the picture).
1103162601
Level:
C
Let \( ABCD \) be a square. Find the dilated image of the square with \( A \) being the centre of dilation and the scale factor \( \frac12 \) (see the picture).
1103235608
Level:
C
The regular hexagonal prism has a volume of \( 324\sqrt3\,\mathrm{cm}^3 \) and the base edge length is equal to the prism’s height. Find the height.
\( 6\,\mathrm{cm} \)
\( 6\sqrt6\,\mathrm{cm} \)
\( 36\sqrt6\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)
1103235607
Level:
C
Find the surface area of a regular hexagonal prism with lateral edge length of \( 10\sqrt3\,\mathrm{cm} \) and a base edge length of \( 6\,\mathrm{cm} \) (see the picture).
\( 468\sqrt3\,\mathrm{cm}^2 \)
\( 414\sqrt3\,\mathrm{cm}^2 \)
\( 168\sqrt3\,\mathrm{cm}^2 \)
\( 408\sqrt3\,\mathrm{cm}^2 \)
1103235606
Level:
C
Find the volume of a regular hexagonal prism with lateral edge length of \( 12\,\mathrm{cm} \) and a base edge length of \( 9\,\mathrm{cm} \) (see the picture).
\( 1458\sqrt3\,\mathrm{cm}^3 \)
\( 243\sqrt3\,\mathrm{cm}^3 \)
\( 1944\sqrt3\,\mathrm{cm}^3 \)
\( 729\sqrt3\,\mathrm{cm}^3 \)
1103235605
Level:
C
A regular hexagonal pyramid has the perimeter of its base \( 12\sqrt3\,\mathrm{cm} \) and its slant height is \( 5\,\mathrm{cm} \). Find the surface area.
\( 48\sqrt3\,\mathrm{cm}^2 \)
\( 72\sqrt3\,\mathrm{cm}^2 \)
\( 30\sqrt3\,\mathrm{cm}^2 \)
\( 96\sqrt3\,\mathrm{cm}^2 \)
1103235604
Level:
C
The area of the base of a regular hexagonal pyramid is \( 54\sqrt3\,\mathrm{cm}^2 \) and the lateral edge is two times the length of the base edge (see the picture). Find the volume of the pyramid.
\( 324\,\mathrm{cm}^3 \)
\( 108\sqrt3\,\mathrm{cm}^3 \)
\( 972\,\mathrm{cm}^3 \)
\( 216\,\mathrm{cm}^3 \)