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

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

• A. 2πr(r + h)
• B. πr²h
• C. 2πrh + 2πr²
• D. π(r² + h²)

Answer: (C)

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} +

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} +