The the surface area of a cylinder with radius r and height h is twice the product of pi and the square of the radius plus twice the product the pie, the radius, and the height

Concept:

(1) Curved surface area of cylinder = Circumference of the base × Height of cylinder

(2) Area of the base = Area of circle = π × (radius)²

(3) Circumference of the base = 2×π× (radius)

Consider a right circular cylinder as given in attached figure

Its height (AB) = H

Its radius (OC) = R

Now, we shall calculate the curved surface area of the cylinder (CSA)

(CSA) = Circumference of the base × Height of cylinder

(CSA) = 2×π×R × H = 2πRH -------(i)

Again, we shall calculate the area of the top and bottom circles

Area of the top and bottom (A) = 2× Area of circle

(A) =2×[ π × (radius)²]

or, (A) = 2×π×R² = 2πR²------------(ii)

Now, we shall calculate the surface area or total surface area of the cylinder.

SA = CSA + A

SA = 2πRH + 2πR²

or, SA = 2πR² + 2πRH

This is the required equation.