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2 answers:
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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.
