A

1003163401

Level: 
A
Find the volume and the surface area of a cube with the edge length of \( 5\,\mathrm{cm} \).
\( V=125\,\mathrm{cm}^3 \), \( S=150\,\mathrm{cm}^2 \)
\( V=15\,\mathrm{cm}^3 \), \( S=25\,\mathrm{cm}^2 \)
\( V=75\,\mathrm{cm}^3 \), \( S=150\,\mathrm{cm}^2 \)
\( V=125\,\mathrm{cm}^3 \), \( S=30\,\mathrm{cm}^2 \)

1003021607

Level: 
A
Consider a right-angled triangle \( ABC \) with the right angle at the vertex \( C \). Calculate the measure of the angle \( CAB \), if the side \( b=9\,\mathrm{cm} \) and the radius of the circumscribed circle \( r=6\,\mathrm{cm} \). Round the result to one decimal place.
\( 41.4^{\circ} \)
\( 48.6^{\circ} \)
\( 36.9^{\circ} \)
\( 48.2^{\circ} \)

1103021606

Level: 
A
In the rectangle \( ABCD \), \( a=6\,\mathrm{cm} \) and the radius of the circumcircle \( r=4\,\mathrm{cm} \) (see the picture). Find the measure of the angle between the diagonals of the rectangle. Round the result to two decimal places.
\( 82.82^{\circ} \)
\( 48.59^{\circ} \)
\( 97.18^{\circ} \)
\( 36.12^{\circ} \)

1003163706

Level: 
A
Let there be a rectangular prism with the length of \( 8\,\mathrm{cm} \), the width of \( 6\,\mathrm{cm} \) and the length of a space diagonal of \( 10\sqrt2\,\mathrm{cm} \). Find the surface area of this prism.
\( 376\,\mathrm{cm}^2 \)
\( 480\,\mathrm{cm}^2 \)
\( \left(96+280\cdot\sqrt2\right)\,\mathrm{cm}^2 \)
\( 480\sqrt2\,\mathrm{cm}^2 \)

1003163705

Level: 
A
Consider a carton storage box in the shape of a cube with the edge length of \( 60\,\mathrm{cm} \). Suppose we want to fill this carton box with small paper boxes of the dimensions: \( 20\,\mathrm{cm} \), \( 5\,\mathrm{cm} \), \( 5\,\mathrm{cm} \). How many of small boxes do we need to fill the big box completely?
\( 432 \)
\( 72 \)
\( 216 \)
\( 75 \)

1003163704

Level: 
A
A rectangular aquarium has length of \( 50\,\mathrm{cm} \) and width of \( 30\,\mathrm{cm} \). Suppose we place a decorative stone in the aquarium and the water level rises by \( 4\,\mathrm{cm} \). What is the volume of the stone?
\( 6\,\mathrm{dm}^3 \)
\( 60\,\mathrm{dm}^3 \)
\( 1.5\,\mathrm{dm}^3 \)
\( 150\,\mathrm{dm}^3 \)

1003163701

Level: 
A
Find the volume and the surface area of a rectangular prism with the edges of lengths \( 8\,\mathrm{cm} \), \( 6\,\mathrm{cm} \), and \( 4\,\mathrm{cm} \).
\( V= 192\,\mathrm{cm}^3 \), \( S= 208\,\mathrm{cm}^2 \)
\( V= 192\,\mathrm{cm}^3 \), \( S= 104\,\mathrm{cm}^2 \)
\( V= 208\,\mathrm{cm}^3 \), \( S= 192\,\mathrm{cm}^2 \)
\( V= 192\,\mathrm{cm}^3 \), \( S= 416\,\mathrm{cm}^2 \)