Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 8 cm 5 cm area of a circle a = πr² 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 $a = \pi r^{2}$, with $r = 8$ cm and $\pi=3.14$. So, $a = 3.14\times8^{2}=3.14\times64 = 200.96$ $cm^{2}$.

Step2: Calculate area of both circles

Since there are two circular bases in a cylinder, the area of both circles is $2\times200.96 = 401.92$ $cm^{2}$.

Step3: Calculate the area of the rectangle (lateral - surface area)

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

Step4: Calculate the total surface area

The total surface area of a cylinder $SA=A_{circles}+A_{l}$. So, $SA = 401.92+251.2=653.12$ $cm^{2}$.

Answer:

Area of both circles: $401.92$ $cm^{2}$
Rectangle: $251.2$ $cm^{2}$
Total SA: $653.12$ $cm^{2}$