Question

what is the surface area of this cylinder?
round your answer to the nearest hundredth.
2 ft
1 ft
square feet
submit

Explanation:

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

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

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

From the problem, \(r = 2\) feet and \(h = 1\) foot.

Step3: Calculate the area of the two circular bases (\(2\pi r^{2}\))

Substitute \(r = 2\) into \(2\pi r^{2}\):

$$
LATEXBLOCK0
$$

Step4: Calculate the lateral surface area (\(2\pi rh\))

Substitute \(r = 2\) and \(h = 1\) into \(2\pi rh\):

$$
LATEXBLOCK1
$$

Step5: Calculate the total surface area

Add the two - parts together: \(S=8\pi + 4\pi=12\pi\)
Using \(\pi\approx3.14159\), we have \(S = 12\times3.14159=37.69908\approx37.70\)

Answer:

\(37.70\)