Question

what is the surface area of a cylinder with base radius 2 and height 9? either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal. 2 9 square units

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 \( h \)

Given that the radius \( r = 2 \) and the height \( h = 9 \).

Step3: Substitute the values into the formula

First, calculate the area of the two circular bases: \( 2\pi r^2 = 2\pi(2)^2 = 2\pi\times4 = 8\pi \).
Then, calculate the lateral (curved) surface area: \( 2\pi rh = 2\pi\times2\times9 = 36\pi \).
Now, add these two parts together: \( S = 8\pi + 36\pi = 44\pi \).
If we use \( \pi = 3.14 \), then \( S = 44\times3.14 = 138.16 \).

Answer:

If in terms of \( \pi \), the answer is \( 44\pi \); if using \( 3.14 \) for \( \pi \), the answer is \( 138.16 \).