# Surface Area of a Cylinder

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A cylinder is a 3-dimensional geometric figure which has congruent circular bases on its top and its bottom. These bases are joined by the curved surface of the cylinder which is elongated to a certain height. The total surface area is the sum of all the surface areas of a given geometric shape. This implies that the total surface area of a cylinder is calculated by adding the areas of the bases of the cylinder and the curved surface area of the cylinder.

Example 1: What is the total surface area of a cylinder whose radius of the circular base is 4m and the height of the cylinder is 6m?

Given: radius, r = 4m

Height of the cylinder, h= 6m

Total Surface area of cylinder, SA = (2* π* r2) + (2* π* r* h)

This gives: Total surface area of the cylinder, SA= (2* π* 42) + (2* π* 4* 6) = 32π+ 48π = 251.3m2

Therefore, the total surface area of the given cylinder is 251.3m2

Example 2: What is the total surface area of a cylinder whose radius of the circular base is 7m and the height of the cylinder is 10m?

Given: radius, r = 7m

Height of the cylinder, h = 10m

Total Surface area of cylinder, SA = (2* π* r2) + (2* π* r* h)

This gives: Total surface area of the cylinder, SA= (2* π* 72) + (2* π* 7* 10) = 98π+ 140π = 747.7m2

Therefore, the total surface area of the given cylinder is 747.7m2