1103068005
Level:
A
Find the missing real constant \( a \) so that the green area and the red area indicated in the picture do equal.
\( a=-2\pi \)
\( a=-\frac32\pi \)
\( a=-\frac{\pi}2 \)
\( a=-3\pi \)
A
1103068004
Level:
A
Find the missing real constant \( a \) so that the ratio of the green and the red area indicated in the picture is \( 4:1 \).
\( a=-\frac{5}3\pi \)
\( a=-2\pi \)
\( a=-\pi \)
\( a=-\frac{5}4\pi \)
1103068003
Level:
A
Find the missing real positive constant \( a \) so that the area of the yellow triangle indicated in the picture is \( 12 \) square units.
\( a=\frac23 \)
\( a=\frac43 \)
\( a=1 \)
The constant \( a \) can not be determined from the picture.
1103068002
Level:
A
Define an unknown real positive constant \( a \) so that the yellow surface indicated in the picture has an area of \( 9 \) square units.
\( a=3 \)
\( a=27 \)
\( a=9 \)
\( a=1 \)
1103068001
Level:
A
Which of the following formulas does NOT express the area of the yellow triangle indicated in the picture?
\( \int\limits_1^ 6(-0.8x+5.8)\,\mathrm{d}x \)
\( \frac12\cdot(5-1)\cdot(6-1)\cdot\sin90^{\circ} \)
\( \frac{4\cdot5}2 \)
\( \int\limits_1^ 6(-0.8x+5.8)\,\mathrm{d}x-5 \)
1003163407
Level:
A
The volume of a cube is \( 8\,\mathrm{l} \). Three-quarters of the cube are filled with water. What is the height of the water level in the cube?
\( 15\,\mathrm{cm} \)
\( 7.5\,\mathrm{cm} \)
\( 16\,\mathrm{cm} \)
\( 24\,\mathrm{cm} \)
1003163406
Level:
A
The volume of a cube is \( 1\,\mathrm{l} \). Find the edge length of this cube.
\( 10\,\mathrm{cm} \)
\( \sqrt{10}\,\mathrm{cm} \)
\( 10\sqrt{10}\,\mathrm{cm} \)
\( 1\,\mathrm{cm} \)
1103163405
Level:
A
The length of a space diagonal of a cube is \( 9\,\mathrm{cm} \). Find the volume of the cube.
\( 81\sqrt3\,\mathrm{cm}^3 \)
\( 9\sqrt3\,\mathrm{cm}^3 \)
\( 27\sqrt3\,\mathrm{cm}^3 \)
\( 81\,\mathrm{cm}^3 \)
1003163404
Level:
A
The numerical value of the volume of a cube equals to the numerical value of the surface area of the cube. What is the numerical value of the length of the cube’s edge?
\( 6 \)
\( \sqrt6 \)
\( 6\sqrt6 \)
\( 1 \)
1103163403
Level:
A
The length of a face diagonal of a cube is \( 6\sqrt2\,\mathrm{cm} \). Find the surface area of the cube.
\( 216\,\mathrm{cm}^2 \)
\( 36\,\mathrm{cm}^2 \)
\( 96\,\mathrm{cm}^2 \)
\( 72\sqrt2\,\mathrm{cm}^2 \)