In the rectangles appearing in the following tasks, we denote 
and 
.
The circumference of the rectangle is 880 cm. Calculate the sides a and b so that the area of the rectangle is the largest.
The rectangle (a = 8 cm, b = 3 cm) is rotated by 
around an axis outside the rectangle that is parallel to the side 
and away from it by d = 2 cm. Calculate the volume and area of the spindle. The result should be accurate.
Point M lies on side BC so that | BM | : | MC | = 1: 3. The intersection of the line DM with the diagonal AC is denoted by P. In what proportion does the point P diagonal AC divide? Write down the ratio | AP | : | PC |.
, 
