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

Explanation:

Step1: Calculate the radius

The diameter is 22 mm, so the radius $r=\frac{22}{2}=11$ mm.

Step2: Calculate the area of the two - bases

The area of a circle is $A_{base}=\pi r^{2}$. The area of two bases $A_{2 - bases}=2\pi r^{2}$. Substitute $r = 11$ mm and $\pi\approx3.14$, we get $A_{2 - bases}=2\times3.14\times11^{2}=2\times3.14\times121 = 759.88$ $mm^{2}$.

Step3: Calculate the lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi rh$. Substitute $r = 11$ mm, $h = 12$ mm and $\pi\approx3.14$, we get $A_{lateral}=2\times3.14\times11\times12=828.96$ $mm^{2}$.

Step4: Calculate the total surface area

The total surface area of a cylinder $A = A_{2 - bases}+A_{lateral}$. So $A=759.88 + 828.96=1588.84$ $mm^{2}$.

Answer:

1588.84