Question

sa = 2(3.14)(1.625²) + 2(3.14)(1.625)(4.25)
sa = 2πr² + 2πrh
4.25 in.
3.25 in.

Explanation:

Step1: Calculate the area of the two - circular bases

The formula for the area of a circle is $A=\pi r^{2}$. Here $r = 1.625$ and we have two circular bases, so the combined area of the bases is $2\times3.14\times(1.625)^{2}$. First, calculate $(1.625)^{2}=1.625\times1.625 = 2.640625$. Then $2\times3.14\times2.640625=2\times8.291525 = 16.58305$.

Step2: Calculate the lateral - surface area

The formula for the lateral - surface area of a cylinder is $A = 2\pi rh$. Here $r = 1.625$ and $h = 4.25$. So $2\times3.14\times1.625\times4.25=6.28\times1.625\times4.25 = 10.205\times4.25=43.37125$.

Step3: Calculate the total surface area

The total surface area $SA$ of a cylinder is the sum of the area of the two bases and the lateral - surface area. So $SA=16.58305 + 43.37125=59.9543$.

Answer:

$59.9543$ square inches.