Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. what is the area of both circles? both circles: ?cm² rectangle: cm² total sa: cm²

Explanation:

Step1: Calculate area of one - circle

The formula for the area of a circle is $A = \pi r^{2}$. Given $r = 8$ cm and $\pi=3.14$, then $A_{1}=\pi r^{2}=3.14\times8^{2}=3.14\times64 = 200.96$ $cm^{2}$.

Step2: Calculate area of both circles

Since there are two circular bases in a cylinder, $A_{circles}=2\times A_{1}=2\times200.96 = 401.92$ $cm^{2}$.

Step3: Calculate the lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Here, $r = 8$ cm and $h = 5$ cm. So $A_{lateral}=2\times3.14\times8\times5=3.14\times80 = 251.2$ $cm^{2}$.

Step4: Calculate the total surface area

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

Answer:

The area of both circles is $401.92$ $cm^{2}$, the area of the rectangle (lateral - surface area) is $251.2$ $cm^{2}$, and the total surface area is $653.12$ $cm^{2}$.