Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 2 cm 14 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 $a = \pi r^{2}$. Given $r = 2$ cm and $\pi=3.14$, then $a = 3.14\times2^{2}=3.14\times4 = 12.56$ $cm^{2}$.

Step2: Calculate area of both circles

Since there are two circular bases in a cylinder, the area of both circles is $2\times a$. Substituting the value of $a$ from Step 1, we get $2\times12.56 = 25.12$ $cm^{2}$.

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, $r = 2$ cm, $h = 14$ cm and $\pi = 3.14$. So $A_{l}=2\times3.14\times2\times14=3.14\times56 = 175.84$ $cm^{2}$.

Step4: Calculate the total surface area

The total surface area of a cylinder $SA$ is the sum of the area of the two circles and the lateral - surface area. So $SA=25.12 + 175.84=200.96$ $cm^{2}$.

Answer:

Both Circles: $25.12$ $cm^{2}$
Rectangle: $175.84$ $cm^{2}$
Total SA: $200.96$ $cm^{2}$