The height of the cylinder is 16. The square-shaped section is parallel to the cylinder

The height of the cylinder is 16. The square-shaped section is parallel to the cylinder axis and at a distance of 6. Find the area of the cylinder’s axial section.

A cylinder is a shape formed by rotating a rectangle around one of its sides.

The axis of a cylinder is a ray passing through the centers of its bases.

The axial section of a cylinder is a plane passing through its axis.

It has the shape of a rectangle, so its area is equal to the product of the diameter of its base and the height:

Sс.section. = d h.

Since the cross-section by a plane has the shape of a square, and its height is 16 cm:

BC = AB = 16 cm.

To calculate the diameter, consider the base of the cylinder.

Point O is the center of the base, as well as the axis of the cylinder, the segments OB and OS are the radii, the segment BC is the secant plane, OH is the distance from the secus plane to the axis.

The triangle ΔBOC is isosceles, since its lateral sides are the radii of the base.

The height of an isosceles triangle divides it into two equal right-angled triangles. Consider one of them, ΔBOH.

BH = HC = BC / 2;

BH = HC = 16/2 = 8 cm.

To calculate the BO hypotenuse, we apply the Pythagorean theorem:

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

BO2 = 62 + 82 = 36 + 64 = 100;

ВO = √100 = 10 cm.

Since the diameter is equal to twice the radius, then:

d = 2r;

d = 2 10 = 20 cm.

Sс.section. = 20 16 = 320 cm2.

Answer: the area of ​​the axial section of the cylinder is 320 cm2.