Question

find the surface area of a cylinder with a base radius of 2 m and a height of 5 m. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit.

Explanation:

Step1: Recall the formula for the surface area of a cylinder

The surface area \( S \) of a cylinder is given by the formula \( S = 2\pi r^2 + 2\pi rh \), where \( r \) is the radius and \( h \) is the height.

Step2: Identify the values of \( r \) and \( h \)

From the problem, the radius \( r = 2 \, \text{m} \) and the height \( h = 5 \, \text{m} \). We are given \( \pi = 3.14 \).

Step3: Calculate the area of the two circular bases

The area of one circular base is \( \pi r^2 \), so for two bases, it is \( 2\pi r^2 \). Substituting \( r = 2 \) and \( \pi = 3.14 \):

$$ 2 \times 3.14 \times (2)^2 = 2 \times 3.14 \times 4 = 25.12 \, \text{m}^2 $$

Step4: Calculate the lateral (curved) surface area

The lateral surface area is \( 2\pi rh \). Substituting \( r = 2 \), \( h = 5 \), and \( \pi = 3.14 \):

$$ 2 \times 3.14 \times 2 \times 5 = 62.8 \, \text{m}^2 $$

Step5: Calculate the total surface area

Add the area of the two bases and the lateral surface area:

$$ S = 25.12 + 62.8 = 87.92 \, \text{m}^2 $$

Answer:

\( 87.92 \, \text{m}^2 \)