Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer.

Explanation:

Step1: Calculate area of two circular bases

The formula for the area of a circle is $A = \pi r^{2}$. Given $r = 8$ cm and $\pi=3.14$. The area of one - circular base is $A_{base}=\pi r^{2}=3.14\times8^{2}=3.14\times64 = 200.96$ $cm^{2}$. The area of two circular bases is $A_{bases}=2\times200.96 = 401.92$ $cm^{2}$.

Step2: Calculate lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi rh$. Here, $r = 8$ cm and $h = 5$ cm. So $A_{lateral}=2\times3.14\times8\times5=251.2$ $cm^{2}$.

Step3: Calculate total surface area

The total surface area of a cylinder $A_{total}=A_{bases}+A_{lateral}$. Substitute the values we found: $A_{total}=401.92 + 251.2=653.12$ $cm^{2}$.

Answer:

$653.12$ $cm^{2}$