In a steel mill, sheet steel is rolled onto cylinders at the end of the production process. When empty, the
radius of one of these cylinders is r0 and the cylinder turns at a constant rotation speed n
during the rolling process. The thickness of the sheet steel is expressed as d.
Which equation expresses the change in a cylinder’s radius r in relation to the time t (in seconds)?

(A)

(A)
incorrect
(B)

(B)
incorrect
(C)

(C)
correct
(D)

(D)
incorrect
Degree of difficulty: average
Solution
To solve this problem, it is necessary to find a formula with which the value of a constantly changing
variable (the radius of the cylinder) can be determined at any given point in time.
Since the cylinder moves at a constant rotation speed n this speed being defined as number of
rotations per unit of time n has to be multiplied by the time t. The result (nt) indicates how
often the cylinder has turned at this point in time.
With every rotation of the cylinder, one layer of steel sheet is added. Therefore, if the product nt is
multiplied by the sheet thickness d, the increase of the cylinder’s radius after t seconds can be
determined.
In order to calculate the total radius, the radius r0 of the empty cylinder at the beginning
of the rolling process must be added to the result.
Alternative C is the only equation which reflects all of these aspects
and is therefore the correct answer.