what is the surface area of this cylinder? use π ≈ 3.14 and round your answer to the nearest hundredth.

Explanation:

Step1: Identify the formula for 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: Determine the values of $r$ and $h$

From the figure, the radius $r = 16$ in and the height $h = 5$ in.

Step3: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^{2}$. So the area of two bases is $2\pi r^{2}=2\times3.14\times16^{2}=2\times3.14\times256 = 1607.68$ square - inches.

Step4: Calculate the lateral surface area

The lateral surface area is $A_{lateral}=2\pi rh$. Substitute $r = 16$ in and $h = 5$ in, we get $A_{lateral}=2\times3.14\times16\times5=502.4$ square - inches.

Step5: Calculate the total surface area

$S=2\pi r^{2}+2\pi rh=1607.68 + 502.4=2110.08$ square - inches.

Answer:

$2110.08$ in²