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. (there is a diagram of a cylinder with radius 2 and height 9)

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 of the base and \( h \) is the height of the cylinder.

Step2: Substitute the given values of \( r = 2 \) and \( h=9 \) 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 to get the total surface area: \( S=8\pi + 36\pi=44\pi \)

If we use \( \pi = 3.14 \), then \( S = 44\times3.14=138.16 \)

Answer:

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