FTCE Professional Education Practice Exam

What is the correct expression for the total surface area of a cylinder?

1. 2(3.14)(rh) + 2(3.14)r^2

2. 1/3(3.14)(r^3)

3. 3.14r^2

4. 1/2PI + B

The correct answer is: 2(3.14)(rh) + 2(3.14)r^2

The total surface area of a cylinder is determined by adding the areas of the two circular bases and the area of the lateral (curved) surface that connects them. The surface area can be derived as follows: 1. The area of one circular base can be calculated using the formula \( \pi r^2 \), where \( r \) is the radius of the base. Since there are two bases, you multiply this area by 2, yielding \( 2\pi r^2 \). 2. The lateral surface area of the cylinder can be calculated with the formula \( 2\pi rh \), where \( h \) is the height of the cylinder. This accounts for the curved surface that wraps around the sides. When you combine both parts, the total surface area \( A \) is given by: \[ A = 2\pi r^2 + 2\pi rh. \] In the context of the question, using \( 3.14 \) as an approximation for \( \pi \) leads to the expression \( 2(3.14)(rh) + 2(3.14)(r^2) \), which matches the correct option. This expression encompasses both the area