Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 4 cm 9 cm what is the area of both circles? both circles: ?cm²

Explanation:

Step1: Calculate area of one - circle

The formula for the area of a circle is $A = \pi r^{2}$. Given $r = 4$ cm and $\pi=3.14$, then $A_1=3.14\times4^{2}=3.14\times16 = 50.24$ $cm^{2}$.

Step2: Calculate area of both circles

Since there are two circular bases in a cylinder, the area of both circles $A_{circles}=2\times A_1$. Substituting the value of $A_1$, we get $A_{circles}=2\times50.24 = 100.48$ $cm^{2}$.

Step3: Calculate lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Substituting $r = 4$ cm, $h = 9$ cm and $\pi = 3.14$, we have $A_{lateral}=2\times3.14\times4\times9=226.08$ $cm^{2}$.

Step4: Calculate total surface area

The total surface area of a cylinder $A_{total}=A_{circles}+A_{lateral}$. Substituting the values of $A_{circles}$ and $A_{lateral}$, we get $A_{total}=100.48 + 226.08=326.56$ $cm^{2}$.

Answer:

$326.56$ $cm^{2}$