a cylinder is shown below. which diagram is a net for the cylinder? what is the surface area of the…

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height. Given that the diameter $d = 8$ ft, so the radius $r=\frac{d}{2}=\frac{8}{2}=4$ ft and the height $h = 14$ ft.

Step2: Calculate the area of the two bases

The area of one circular base is $A_{base}=\pi r^2$. Substituting $r = 4$ ft, we get $A_{base}=\pi\times(4)^2=16\pi$ square - feet. The area of two bases is $A_{2bases}=2\times16\pi = 32\pi$ square - feet.

Step3: Calculate the lateral - surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi rh$. Substituting $r = 4$ ft and $h = 14$ ft, we get $A_{lateral}=2\pi\times4\times14=112\pi$ square - feet.

Step4: Calculate the total surface area

$S=A_{2bases}+A_{lateral}=32\pi + 112\pi=144\pi$ square - feet.

Step5: Substitute $\pi\approx3.14$

$S\approx144\times3.14 = 452.16$ square - feet.

Step6: Round to the nearest tenth

Rounding $452.16$ to the nearest tenth gives $452.2$ square - feet.

Answer:

$452.2$