meg is an engineer who designs watch batteries. the battery shes currently designing is shaped like a…

Explanation:

Step1: Find the radius

The diameter $d = 6.8$ mm, so the radius $r=\frac{d}{2}=\frac{6.8}{2}=3.4$ 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 $A_{2bases}=2\pi r^{2}$. Substitute $r = 3.4$ mm and $\pi\approx3.14$: $A_{2bases}=2\times3.14\times3.4^{2}=2\times3.14\times11.56 = 72.5344$ $mm^{2}$.

Step3: Calculate the lateral surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi rh$. Substitute $r = 3.4$ mm, $h = 2.1$ mm and $\pi\approx3.14$: $A_{lateral}=2\times3.14\times3.4\times2.1=44.8744$ $mm^{2}$.

Step4: Calculate the total surface area

The total surface area of a cylinder $A = A_{2bases}+A_{lateral}$. So $A=72.5344 + 44.8744=117.4088\approx117$ $mm^{2}$.

Answer:

117