# The height of the cylinder is 2 cm less than its radius. The lateral surface area of the cylinder

**The height of the cylinder is 2 cm less than its radius. The lateral surface area of the cylinder is 160π cm2. Find the surface area of the ball.**

The area of the lateral surface of the cylinder is equal to the product of the circumference of the base of the cylinder by the height:

S = 2πrh.

The height of this cylinder is 2 centimeters less than its radius, so we express it as:

x – length of height h;

x + 2 – base radius r;

Let’s make the equation:

2π x (x + 2) = 160π;

x (x + 2) = 80;

x ^ 2 + 2x = 80;

x ^ 2 + 2x – 80 = 0;

D = b ^ 2 – 4ac;

D = 4 – (- 320) = 4 + 320 = 324 = 182;

Since our value can only be positive, the solution will have one thing:

x = (- b + √D) / 2a;

x = (- 2 + 18) / 2 = 16/2 = 8;

h = 8 cm;

r = 8 + 2 = 10 cm.

Answer: the radius is 10 cm, the height is 8 cm.