Find the areas of the lateral and full surfaces of the cylinder, if r = 2cm; h = 10 cm.

It is known from the condition that the cylinder is given by the radius of the base R = 2 cm and the height H = 10 cm. And we need to find the areas of the lateral and full surfaces of the cylinder.

Let’s start by recalling the formula for finding the lateral surface area of a cylinder:

S_side. = 2nRH.

We substitute the values into the formula and perform the calculation:

S_side. = 2 * 3.14 * 2 * 10 = 125.6 cm ^ 2.

Full cylinder surface area:

S_pol = S_bok + 2nR ^ 2 = 125.6 + 2 * 3.14 * 2 ^ 2 = 125.6 + 25.12 = 150.72 cm ^ 2.

Answer: 150.72 cm ^ 2.