# In a cylinder with a height of 6 cm, a parallel section is drawn at a distance of 4 cm from it.

In a cylinder with a height of 6 cm, a parallel section is drawn at a distance of 4 cm from it. Find the radius of the cylinder if the area of the specified section is 36 cm2.

Since the cutting plane has the shape of a rectangle, its area will be equal to the product of height and width:

S = AB · BC.

Based on this:

BC = S / AB;

BC = 36/6 = 6 cm.

Consider the triangle ΔBOC. Point O is the center of the base of the cylinder, as well as the vertex of this triangle. Segments BO and OC are the radii of the cylinder, as well as the lateral sides of the triangle. Based on this, we see that this triangle is isosceles.

The OH segment is the distance from the center to the secant, as well as the height of this triangle.

The height of this triangle divides it into two equal rectangular ones, in which:

DO = OC;

BH = HC = BC / 2;

BH = HC = 6/2 = 3 cm.

Take, for example, the triangle ΔBOН.

To calculate the hypotenuse of ВO, we apply the Pythagorean theorem:

BO^2 = OH^2 + BH^2;

BO^2 = 4^2 + 3^2 = 16 + 9 = 25;

ВO = √25 = 5 cm.

The ВO segment is the radius of the base of this cylinder.