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 $r = 3$ cm and $\pi=3.14$, then $A_1=3.14\times3^{2}=3.14\times9 = 28.26$ $cm^{2}$.

Step2: Calculate area of both circles

Since there are two circular bases in a cylinder, the area of both circles $A_{circles}=2\times A_1=2\times28.26 = 56.52$ $cm^{2}$.

Step3: Calculate the lateral - surface area (rectangle)

The formula for the lateral - surface area of a cylinder (which is in the shape of a rectangle when unrolled) is $A_{rectangle}=2\pi r h$. Here, $r = 3$ cm, $h = 13$ cm and $\pi=3.14$. So $A_{rectangle}=2\times3.14\times3\times13=244.92$ $cm^{2}$.

Step4: Calculate the total surface area

The total surface area of the cylinder $A_{total}=A_{circles}+A_{rectangle}=56.52 + 244.92=301.44$ $cm^{2}$.

Answer:

Both Circles: $56.52$ $cm^{2}$
Rectangle: $244.92$ $cm^{2}$
Total SA: $301.44$ $cm^{2}$