Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 3 cm 6 cm what is the area of both circles? both circles:? cm² rectangle: cm² total sa: cm² area of a circle a = πr²

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 $a = 3.14\times3^{2}=3.14\times9 = 28.26$ $cm^{2}$.

Step2: Calculate area of both circles

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

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

The formula for the lateral - surface area of a cylinder (the area of the rectangle) is $A_{l}=2\pi r h$. Here, $r = 3$ cm, $h = 6$ cm, and $\pi = 3.14$. So $A_{l}=2\times3.14\times3\times6=113.04$ $cm^{2}$.

Step4: Calculate the total surface area

The total surface area (SA) of a cylinder is the sum of the area of the two circles and the lateral - surface area. So $SA=56.52 + 113.04=169.56$ $cm^{2}$.

Answer:

Both Circles: $56.52$ $cm^{2}$
Rectangle: $113.04$ $cm^{2}$
Total SA: $169.56$ $cm^{2}$