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.