The height of the cylinder is 10 cm, the cross-sectional area of the cylinder with a plane parallel

The height of the cylinder is 10 cm, the cross-sectional area of the cylinder with a plane parallel to the axis of the cylinder and located at a distance of 6 cm from it = 160 cm ^ 2, calculate the total surface area

A cylinder is a body created by rotating a rectangle around its side.

The axial section of a cylinder is a plane passing through its axis, that is, through the centers of its bases.

The total surface area of ​​the cylinder is equal to the sum of the area of ​​its lateral surface and twice the area of ​​its bases:

Sp.p. = 2πrh + 2πr2.

Find the radius of the base of this cylinder. To do this, consider its foundation.

Point O is the center of its base, as well as the axis of the cylinder. Side AB of the plane ABCD is the base of the triangle ΔABO formed by the plane, the center of the base, and also the radii. This means that this triangle is isosceles.

Since the ABCD plane is a rectangle with an area of ​​160 cm2 and a length of 10 cm, the width AB will be equal to:

SABSD = AB * BC;

AB = SABCD / BC;

AB = 160/10 = 16 cm.

The height OH divides it into two equal right-angled triangles. Consider one of them ΔAOH.

AH = HB = AB / 2;

AH = HB = 16/2 = 8 cm.

To calculate the AO side, we apply the Pythagorean theorem:

AO ^ 2 = AH ^ 2 + HO ^ 2;

AO ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100;

AO = √100 = 10 cm.

Sp.p. = (2 * 3.14 * 10 * 10) + (2 * 3.14 * 100) = 628 + 628 = 1256 cm2.

Answer: the total surface area of ​​the cylinder is 1256 cm2.