What is the total surface area of a cylinder calculated as?

The total surface area of a cylinder is calculated by adding the areas of the two circular bases and the area of the curved surface that connects those bases.

To break it down:

1. Area of the circular bases: A cylinder has two bases, and each base is a circle with a radius ( r ). The area of one circle is calculated using the formula ( \pi r^2 ). Since there are two bases, the total area of the bases combined is ( 2 \times \pi r^2 ), or ( 2\pi r^2 ).

2. Area of the curved surface: The curved surface area can be visualized as the area of a rectangle that has been wrapped around the circular bases. The height of this rectangle is the height of the cylinder ( h ), and the width is the circumference of the base, which is ( 2\pi r ). Therefore, the area of the curved surface is given by ( 2\pi rh ).

Finally, to find the total surface area, you add the area of the two bases to the area of the curved surface:

[ \text{Total Surface Area} = \text{Area of bases} +