what is the surface area of this cylinder? use $piapprox3.14$ and round your answer to the nearest…

Explanation:

Step1: Identify the formula for cylinder surface area

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. Here, the diameter is 6 mm, so the radius $r=\frac{6}{2}=3$ mm and the height $h = 3$ mm.

Step2: Calculate the area of the two - circular bases

The area of one - circular base is $A_{base}=\pi r^2$. Substituting $r = 3$ mm, we get $A_{base}=\pi\times(3)^2=9\pi$ square mm. The area of two - circular bases is $A_{2bases}=2\pi r^2=2\times\pi\times(3)^2 = 18\pi$ square mm.

Step3: Calculate the lateral surface area

The lateral surface area of a cylinder is $A_{lateral}=2\pi rh$. Substituting $r = 3$ mm and $h = 3$ mm, we get $A_{lateral}=2\pi\times3\times3=18\pi$ square mm.

Step4: Calculate the total surface area

$S=A_{2bases}+A_{lateral}=18\pi + 18\pi=36\pi$ square mm.

Step5: Substitute the value of $\pi$ and round

Substitute $\pi\approx3.14$ into $S = 36\pi$. Then $S\approx36\times3.14 = 113.04$ square mm.

Answer:

$113.04$