Question

find the surface area of a cylinder with a base radius of 2 cm and a height of 7 cm. 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 given values

We are given that \( r = 2 \) cm, \( h = 7 \) cm, and \( \pi = 3.14 \).

Step3: Calculate the area of the two circular bases

First, calculate \( 2\pi r^2 \). Substitute \( r = 2 \) and \( \pi = 3.14 \):

$$ 2 \times 3.14 \times (2)^2 = 2 \times 3.14 \times 4 = 25.12 $$

Step4: Calculate the lateral (curved) surface area

Next, calculate \( 2\pi rh \). Substitute \( r = 2 \), \( h = 7 \), and \( \pi = 3.14 \):

$$ 2 \times 3.14 \times 2 \times 7 = 87.92 $$

Step5: Add the two areas together to get the total surface area

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

$$ 25.12 + 87.92 = 113.04 $$

Answer:

\( 113.04 \, \text{cm}^2 \)