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 values of \( r \), \( h \), and \( \pi \)

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

Step3: Calculate the area of the two circular bases

The area of one circular base is \( \pi r^2 \), so the area of two bases is \( 2\pi r^2 \). Substituting the values, we get:
\[
2\times3.14\times(2)^2 = 2\times3.14\times4 = 25.12
\]

Step4: Calculate the lateral (curved) surface area

The lateral surface area is \( 2\pi rh \). Substituting the values, we get:
\[
2\times3.14\times2\times7 = 87.92
\]

Step5: Add the areas of the two parts to get the total surface area

Adding the area of the two bases and the lateral surface area:
\[
25.12 + 87.92 = 113.04
\]

Answer:

\( 113.04 \) square centimeters (or \( 113.04 \, \text{cm}^2 \))