The fomula for the surface area, S, of a cylinder, is S = 2nr2 2nrh, where his the height of the cylinder, and r is the radius of the base of the cylinder.

S = 2πr² + 2πrh = 2πr(r + h)

Step-by-step explanation:

The formula for the surface area of a cylinder is the sum of the area of the base and the lateral faces.

Mathematically,

surface area = base area + lateral area

A cylinder has 2 base which are circular therefore, the sum of the area of the base is πr² + πr² = 2πr².

The lateral area is the curved surface area of the cylinder which is the multiplication of the height and the circumference .  

curved surface area = h × circumference = 2πrh

surface area = 2πr² + 2πrh = 2πr(r + h)

S = 2πr² + 2πrh = 2πr(r + h)

The surface area can be calculated if you know the height of the cylinder and the radius. example r = 5 m and h = 10 m

Using the formula

S = 2πr² + 2πrh = 2πr(r + h)

S= 2 × π × 5(5 + 10)

S = 10π(15)

S = 150π m²

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